# Recent questions tagged calculus

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Evaluate $\sqrt{x^{2}+y^{2}+1}=?$
Evaluate $\sqrt{x^{2}+y^{2}+1}=?$\begin{aligned} &amp;x^{2}=17 x+y \\ &amp;y^{2}=x+17 y \\ &amp;x \neq y \\ &amp;\sqrt{x^{2}+y^{2}+1}=? \end{aligned} ...
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Solve the equation $\sqrt{x+18}=x-2$
Solve the equation $\sqrt{x+18}=x-2$Solve the equation $\sqrt{x+18}=x-2$ ...
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Evaluate the following expression when $a=3$ and $b=-8: 3 a^{2}-7 b$
Evaluate the following expression when $a=3$ and $b=-8: 3 a^{2}-7 b$Evaluate the following expression when $a=3$ and $b=-8: 3 a^{2}-7 b$ ...
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Name the property demonstrated by the equation. $11+(8+6)=(y+8)+6$. And find the value of $y ?$
Name the property demonstrated by the equation. $11+(8+6)=(y+8)+6$. And find the value of $y ?$Name the property demonstrated by the equation. $11+(8+6)=(y+8)+6$. And find the value of $y ?$ ...
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What is the value of $6(2 b-4)$ when $b=5$ ?
What is the value of $6(2 b-4)$ when $b=5$ ?What is the value of $6(2 b-4)$ when $b=5$ ? ...
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What are the derivatives for bases other than $e$?
What are the derivatives for bases other than $e$?What are the derivatives for bases other than $e$? ...
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The determinant of matrix $\mathrm{Q}=\left(\begin{array}{cc}8 & 12 \\ x-4 & x\end{array}\right)$ is 8. Find
The determinant of matrix $\mathrm{Q}=\left(\begin{array}{cc}8 & 12 \\ x-4 & x\end{array}\right)$ is 8. FindThe determinant of matrix $\mathrm{Q}=\left(\begin{array}{cc}8 &amp; 12 \\ x-4 &amp; x\end{array}\right)$ is 8. Find (i) the value of $x$, (ii) t ...
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What is the definition of area in calculus?
What is the definition of area in calculus?What is the definition of area in calculus? ...
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What are the four important concepts in calculus?
What are the four important concepts in calculus?What are the four important concepts in calculus? ...
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Evaluate $\large{\int}{\dfrac{\sin{(\sqrt{x}+a)} \cdot e^{\sqrt{x}} }{ \sqrt{x}}}dx$
Evaluate $\large{\int}{\dfrac{\sin{(\sqrt{x}+a)} \cdot e^{\sqrt{x}} }{ \sqrt{x}}}dx$Evaluate $\large{\int}{\dfrac{\sin{(\sqrt{x}+a)} \cdot e^{\sqrt{x}} }{ \sqrt{x}}}dx$ ...
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Find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ for the following function. $x^{2} \sin \left(y^{3}\right)+x \mathbf{e}^{3 z}-\cos \left(z^{2}\right)=3 y-6 z+8$Find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ for the following function. \ x^{2} \sin \left(y^{3}\right)+x \mathbf{e} ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $z=\frac{p^{2}(r+1)}{t^{3}}+p r \mathbf{e}^{2 p+3 r+4 t}$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $z=\frac{p^{2}(r+1)}{t^{3}}+p r \mathbf{e}^{2 p+3 r+4 t}$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ z=\frac{p^{2}(r+1)}{t^{3}}+p r \mathbf{e}^{2 p+3 r+4 t} \ ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $R(x, y)=\frac{x^{2}}{y^{2}+1}-\frac{y^{2}}{x^{2}+y}$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $R(x, y)=\frac{x^{2}}{y^{2}+1}-\frac{y^{2}}{x^{2}+y}$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ R(x, y)=\frac{x^{2}}{y^{2}+1}-\frac{y^{2}}{x^{2}+y} \ ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $g(s, t, v)=t^{2} \ln (s+2 t)-\ln (3 v)\left(s^{3}+t^{2}-4 v\right)$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $g(s, t, v)=t^{2} \ln (s+2 t)-\ln (3 v)\left(s^{3}+t^{2}-4 v\right)$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ g(s, t, v)=t^{2} \ln (s+2 t)-\ln (3 v)\left(s^{3}+t^{2}-4 v\r ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $f(x, z)=\mathbf{e}^{-x} \sqrt{z^{4}+x^{2}}-\frac{2 x+3 z}{4 z-7 x}$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $f(x, z)=\mathbf{e}^{-x} \sqrt{z^{4}+x^{2}}-\frac{2 x+3 z}{4 z-7 x}$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ f(x, z)=\mathbf{e}^{-x} \sqrt{z^{4}+x^{2}}-\frac{2 x+3 z}{4 z ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $f(u, v)=u^{2} \sin \left(u+v^{3}\right)-\sec (4 u) \tan ^{-1}(2 v)$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $f(u, v)=u^{2} \sin \left(u+v^{3}\right)-\sec (4 u) \tan ^{-1}(2 v)$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ f(u, v)=u^{2} \sin \left(u+v^{3}\right)-\sec (4 u) \tan ^{-1} ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $f(u, v, p, t)=8 u^{2} t^{3} p-\sqrt{v} p^{2} t^{-5}+2 u^{2} t+3 p^{4}-v$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $f(u, v, p, t)=8 u^{2} t^{3} p-\sqrt{v} p^{2} t^{-5}+2 u^{2} t+3 p^{4}-v$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ f(u, v, p, t)=8 u^{2} t^{3} p-\sqrt{v} p^{2} t^{-5}+2 u^{2} t ...
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Find all the $1^{\text {st }}$ order partial derivatives of the following function. $w=\cos \left(x^{2}+2 y\right)-\mathbf{e}^{4 x-z^{4} y}+y^{3}$
Find all the $1^{\text {st }}$ order partial derivatives of the following function. $w=\cos \left(x^{2}+2 y\right)-\mathbf{e}^{4 x-z^{4} y}+y^{3}$Find all the $1^{\text {st }}$ order partial derivatives of the following function. \ w=\cos \left(x^{2}+2 y\right)-\mathbf{e}^{4 x-z^{4} y}+y^{3} ...
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Find ∂w/∂x at the point (2,-1,1) if w=x^2+y^2+z^2 , z^3 - xy+ yz+y^3 = 0 if x and y are independent variables
Find ∂w/∂x at the point (2,-1,1) if w=x^2+y^2+z^2 , z^3 - xy+ yz+y^3 = 0 if x and y are independent variablesThis is a question under partial differentiation under functions of many variables ...
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Solve $\ln (x+1)-\ln (x)=\ln 4$
Solve $\ln (x+1)-\ln (x)=\ln 4$Solve $\ln (x+1)-\ln (x)=\ln 4$ ...
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Find the derivative of $\sqrt{3x^2+1}$ by the 1st principle method.
Find the derivative of $\sqrt{3x^2+1}$ by the 1st principle method.Find the derivative of $\sqrt{3x^2+1}$ by the 1st principle method. ...
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If $f$ is $n+1$ times continuously differentiable, then
If $f$ is $n+1$ times continuously differentiable, thenIf $f$ is $n+1$ times continuously differentiable, then ...
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A function $f(x)$ is square-integrable if
A function $f(x)$ is square-integrable ifA function $f(x)$ is square-integrable if ...
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If $f(x)$ is continuous or piecewise continuous on $[a, b]$, then
If $f(x)$ is continuous or piecewise continuous on $[a, b]$, thenIf $f(x)$ is continuous or piecewise continuous on $a, b$, then ...
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For $f(x)$ monotonic and $\phi(x)$ integrable on $[a, b]$, there exists $c \in[a, b]$, such that
For $f(x)$ monotonic and $\phi(x)$ integrable on $[a, b]$, there exists $c \in[a, b]$, such thatFor $f(x)$ monotonic and $\phi(x)$ integrable on $a, b$, there exists $c \ina, b$, such that ...
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For $f(x)$ continuous and $\phi(x) \geq 0$ and integrable on $[a, b]$, there exists $c \in[a, b]$, such that
For $f(x)$ continuous and $\phi(x) \geq 0$ and integrable on $[a, b]$, there exists $c \in[a, b]$, such thatFor $f(x)$ continuous and $\phi(x) \geq 0$ and integrable on $a, b$, there exists $c \ina, b$, such that ...
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If $\phi^{\prime}(x)$ is continuous or piecewise continuous, then
If $\phi^{\prime}(x)$ is continuous or piecewise continuous, thenIf $\phi^{\prime}(x)$ is continuous or piecewise continuous, then ...
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What is an indefinite integral?
What is an indefinite integral?What is an indefinite integral? ...
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State Leibniz’s Formula
State Leibniz’s FormulaState Leibniz&amp;rsquo;s Formula ...
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What does the mean value theorem say?
What does the mean value theorem say?What does the mean value theorem say? ...
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What do we mean by higher derivatives in mathematics?
What do we mean by higher derivatives in mathematics?What do we mean by higher derivatives in mathematics? ...
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The derivative $f^{\prime}(x)$ of $f(x)$ is defined by
The derivative $f^{\prime}(x)$ of $f(x)$ is defined byThe derivative $f^{\prime}(x)$ of $f(x)$ is defined by ...
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What does the binomial theorem state?
What does the binomial theorem state?What does the binomial theorem state? ...
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$2 x+(-2)=x^{2} .$ Find $x$
$2 x+(-2)=x^{2} .$ Find $x$$2 x+(-2)=x^{2} .$ Find $x$ ...
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A soft-drink company introduces a new beverage. One month later, the company wants to know whether its marketing strategies have reached young adults of ages 18-20.
A soft-drink company introduces a new beverage. One month later, the company wants to know whether its marketing strategies have reached young adults of ages 18-20.A soft-drink company introduces a new beverage. One month later, the company wants to know whether its marketing strategies have reached young adults ...
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You consult Joe the bookie as to the form in the $2.30$ at Ayr. He tells you that, of 16 runners, the favourite has probability $0.3$ of winning, ...
You consult Joe the bookie as to the form in the $2.30$ at Ayr. He tells you that, of 16 runners, the favourite has probability $0.3$ of winning, ...You consult Joe the bookie as to the form in the $2.30$ at Ayr. He tells you that, of 16 runners, the favourite has probability $0.3$ of winning, ...
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Complete the number sentence to make the statement true, by filling in <; > or =: 22101   _____   22110
Complete the number sentence to make the statement true, by filling in <; > or =: 22101   _____   22110Complete the number sentence to make the statement true, by filling in &lt;; &gt; or =: 22101 &nbsp;&nbsp;_____ &nbsp;&nbsp;22110 ...
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Solve for $x$ if $\frac{3 x+1}{2}=5$
Solve for $x$ if $\frac{3 x+1}{2}=5$Solve for $x$ if $\frac{3 x+1}{2}=5$ ...
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Subtract $\quad-4 x+8 y+6$ from $2 x+3 y-1$
Subtract $\quad-4 x+8 y+6$ from $2 x+3 y-1$Subtract $\quad-4 x+8 y+6$ from $2 x+3 y-1$ ...
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The HCF of $12 x^{2} y ; 42 x^{3} y^{2} ; 27 x y$ is:
The HCF of $12 x^{2} y ; 42 x^{3} y^{2} ; 27 x y$ is:The HCF of $12 x^{2} y ; 42 x^{3} y^{2} ; 27 x y$ is: ...
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State the definition of the derivative of a function $g$ at a number $x$.
State the definition of the derivative of a function $g$ at a number $x$.State the definition of the derivative of a function $g$ at a number $x$. ...
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If $x^{5}+y^{5}=1$, what is $y^{\prime}$ in terms of $x$ and $y$ ?
If $x^{5}+y^{5}=1$, what is $y^{\prime}$ in terms of $x$ and $y$ ?If $x^{5}+y^{5}=1$, what is $y^{\prime}$ in terms of $x$ and $y$ ? ...
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Differentiate $f(x)=\dfrac{\ln x}{x}$, for $x>0$
Differentiate $f(x)=\dfrac{\ln x}{x}$, for $x>0$Differentiate $f(x)=\dfrac{\ln x}{x}$, for $x&gt;0$ ...
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Derive the differentiation formula $\frac{d}{d x}[\arcsin x]=\frac{1}{\sqrt{1-x^{2}}}$.
Derive the differentiation formula $\frac{d}{d x}[\arcsin x]=\frac{1}{\sqrt{1-x^{2}}}$.Derive the differentiation formula $\dfrac{d}{d x}\arcsin x=\dfrac{1}{\sqrt{1-x^{2}}}$. ...
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Prove that $f(x)=\frac{1}{(x+1)^{2}}-2 x+\sin x$ has exactly one positive root.
Prove that $f(x)=\frac{1}{(x+1)^{2}}-2 x+\sin x$ has exactly one positive root.Prove that $f(x)=\dfrac{1}{(x+1)^{2}}-2 x+\sin x$ has exactly one positive root. ...
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Show that the equation $x^{3}+9 x+5=0$ has exactly one real solution.
Show that the equation $x^{3}+9 x+5=0$ has exactly one real solution.Show that the equation $x^{3}+9 x+5=0$ has exactly one real solution. ...
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Show that $y=3 x^{3}+2 x+12$ has a unique root.
Show that $y=3 x^{3}+2 x+12$ has a unique root.Show that $y=3 x^{3}+2 x+12$ has a unique root. ...
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If a person has a blood alcohol concentration of $1 \%$, how long should she/he wait before driving in order not to disobey the law. You may need the value $\ln 2 \approx 0.7$. The concentration of alcohol (in \%) in the blood, $C(t)$, obeys the decay differential equation: \ \frac{d C}{d t}=-\frac{1}{k} C, \ where ...
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Find $f$ if $f^{\prime \prime}(t)=2 e^{t}+3 \sin t$ and $f(0)=0, f^{\prime}(0)=0$.
Find $f$ if $f^{\prime \prime}(t)=2 e^{t}+3 \sin t$ and $f(0)=0, f^{\prime}(0)=0$.Find $f$ if $f^{\prime \prime}(t)=2 e^{t}+3 \sin t$ and $f(0)=0, f^{\prime}(0)=0$. ...
For each case compute the indefinite integral.For each case compute the indefinite integral. (a) $\int(1-x)^{8} d$ (b) $\int \tan ^{2} x d x$ (c) $\int \frac{d x}{2+x^{2}}$ (d) \(\int e^{2 ...