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Recent questions tagged calculus


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Evaluate \(\sqrt{x^{2}+y^{2}+1}=?\)
1 answer 40 views
Evaluate \(\sqrt{x^{2}+y^{2}+1}=?\)\begin{aligned} &x^{2}=17 x+y \\ &y^{2}=x+17 y \\ &x \neq y \\ &\sqrt{x^{2}+y^{2}+1}=? \end{aligned} ...
by Pieter Gold Status
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asked in Mathematics May 6
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Solve the equation \(\sqrt{x+18}=x-2\)
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Solve the equation \(\sqrt{x+18}=x-2\)Solve the equation \(\sqrt{x+18}=x-2\) ...
by Pieter Gold Status
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asked in Mathematics May 2
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Evaluate the following expression when \(a=3\) and \(b=-8: 3 a^{2}-7 b\)
1 answer 28 views
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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 \(b=5\) ?
2 answers 33 views
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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asked in Mathematics Apr 26
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What are the derivatives for bases other than \(e\)?
1 answer 34 views
What are the derivatives for bases other than \(e\)?What are the derivatives for bases other than \(e\)? ...
by MathsGee Platinum
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asked in Mathematics Apr 6
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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
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The determinant of matrix \(\mathrm{Q}=\left(\begin{array}{cc}8 & 12 \\ x-4 & x\end{array}\right)\) is 8. FindThe determinant of matrix \(\mathrm{Q}=\left(\begin{array}{cc}8 & 12 \\ x-4 & x\end{array}\right)\) is 8. Find (i) the value of \(x\), (ii) t ...
by Pieter Gold Status
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asked in Mathematics Apr 1
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What is the definition of area in calculus?
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What is the definition of area in calculus?What is the definition of area in calculus? ...
by Pieter Gold Status
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asked in Mathematics Mar 31
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What are the four important concepts in calculus?
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What are the four important concepts in calculus?What are the four important concepts in calculus? ...
by Pieter Gold Status
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asked in Mathematics Mar 31
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Evaluate \(\large{\int}{\dfrac{\sin{(\sqrt{x}+a)} \cdot e^{\sqrt{x}} }{ \sqrt{x}}}dx\)
1 answer 48 views
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Find all the \(1^{\text {st }}\) order partial derivatives of the following function. \[ z=\frac{p^{2}(r+1)}{t^{3}}+p r \mathbf{e}^{2 p+3 r+4 t} \]

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Find all the \(1^{\text {st }}\) order partial derivatives of the following function. \[ R(x, y)=\frac{x^{2}}{y^{2}+1}-\frac{y^{2}}{x^{2}+y} \]

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Find all the \(1^{\text {st }}\) order partial derivatives of the following function. \[ g(s, t, v)=t^{2} \ln (s+2 t)-\ln (3 v)\left(s^{3}+t^{2}-4 v\right) \]

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Find all the \(1^{\text {st }}\) order partial derivatives of the following function. \[ f(x, z)=\mathbf{e}^{-x} \sqrt{z^{4}+x^{2}}-\frac{2 x+3 z}{4 z-7 x} \]

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Find all the \(1^{\text {st }}\) order partial derivatives of the following function. \[ f(u, v)=u^{2} \sin \left(u+v^{3}\right)-\sec (4 u) \tan ^{-1}(2 v) \]

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Find all the \(1^{\text {st }}\) order partial derivatives of the following function. \[ w=\cos \left(x^{2}+2 y\right)-\mathbf{e}^{4 x-z^{4} y}+y^{3} \]

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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

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Solve \(\ln (x+1)-\ln (x)=\ln 4\)
1 answer 204 views
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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
1 answer 66 views
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A function \(f(x)\) is square-integrable if
1 answer 73 views
A function \(f(x)\) is square-integrable ifA function \(f(x)\) is square-integrable if ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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If \(f(x)\) is continuous or piecewise continuous on \([a, b]\), then
1 answer 90 views
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For \(f(x)\) monotonic and \(\phi(x)\) integrable on \([a, b]\), there exists \(c \in[a, b]\), such that
1 answer 74 views
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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

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If \(\phi^{\prime}(x)\) is continuous or piecewise continuous, then
1 answer 67 views
If \(\phi^{\prime}(x)\) is continuous or piecewise continuous, thenIf \(\phi^{\prime}(x)\) is continuous or piecewise continuous, then ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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What is an indefinite integral?
1 answer 46 views
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State Leibniz’s Formula
1 answer 41 views
State Leibniz’s FormulaState Leibniz’s Formula ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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What does the mean value theorem say?
1 answer 61 views
What does the mean value theorem say?What does the mean value theorem say? ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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What do we mean by higher derivatives in mathematics?
1 answer 51 views
What do we mean by higher derivatives in mathematics?What do we mean by higher derivatives in mathematics? ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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The derivative \(f^{\prime}(x)\) of \(f(x)\) is defined by
1 answer 191 views
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What does the binomial theorem state?
1 answer 76 views
What does the binomial theorem state?What does the binomial theorem state? ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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\(2 x+(-2)=x^{2} .\) Find \(x\)
1 answer 47 views
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Complete the number sentence to make the statement true, by filling in <; > or =: 22101   _____   22110
0 answers 81 views
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Solve for \(x\) if \(\frac{3 x+1}{2}=5\)
0 answers 44 views
Solve for \(x\) if \(\frac{3 x+1}{2}=5\)Solve for \(x\) if \(\frac{3 x+1}{2}=5\) ...
by Pieter Gold Status
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asked in Mathematics Feb 5
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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:
0 answers 42 views
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State the definition of the derivative of a function \(g\) at a number \(x\).
0 answers 114 views
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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 \(x>0\)
0 answers 146 views
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Derive the differentiation formula \(\frac{d}{d x}[\arcsin x]=\frac{1}{\sqrt{1-x^{2}}}\).
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Prove that \(f(x)=\frac{1}{(x+1)^{2}}-2 x+\sin x\) has exactly one positive root.
0 answers 59 views
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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.
0 answers 45 views
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Find \(f\) if \(f^{\prime \prime}(t)=2 e^{t}+3 \sin t\) and \(f(0)=0, f^{\prime}(0)=0\).
0 answers 130 views
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For each case compute the indefinite integral.
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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 ...
by Pieter Gold Status
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asked in Mathematics Feb 4
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