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Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if \[ y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \]
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Given \[ y=\sqrt{x^{7}}-\frac{5}{x^{3}} \] Which of the following is equivalent to \(y\) ?
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Given \[ y=\sqrt{x^{7}}-\frac{5}{x^{3}} \] Which of the following is equivalent to \(y\) ?Given \ y=\sqrt{x^{7}}-\frac{5}{x^{3}} \ Which of the following is equivalent to \(y\) ? \begin{align} \begin{array}{|l|l|} \hline \text { A } &amp ...
by MathsGee Platinum
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asked in Mathematics Jan 15
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Differentiate \(g(t)=4(t+1)^{2}(t-3)\) with respect to \(t\)
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Differentiate the function \(m=\frac{3}{2} n^{4}-1\)
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Differentiate the function \(y=3 x^{5}\)
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\begin{equation} \text { Consider the system } A X=B, \text { where } X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right] \text {. } \end{equation}

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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has   A. no extremum, B. exactly one maximum, C. exactly one minimum, D. exactly ...
by MathsGee Platinum
(103,030 points)
asked in Mathematics Jan 13
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ is
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ isThe function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ is   A. strictly increasing on $(-\infty, \infty)$,   B. strictly increasing on $(-\infty ...
by MathsGee Platinum
(103,030 points)
asked in Mathematics Jan 13
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has ...
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has ...The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has   A. no point of inflection and is concave up on $(-\infty, \infty)$,   B. no point o ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Prove Rolle's Theorem under the assumption that for the function $f$ on $[a, b]$ you have $f(x)>f(a)$ for some $x$ in the domain of $f$.
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Sketch the graph of $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$
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Sketch the graph of $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$Sketch the graph of $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Evaluate the integral: $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$
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Evaluate the integral: $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$Evaluate the integral:   $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$ ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Evaluate the integral: $\int_{0}^{\pi} 2 x \cos 2 x d x$
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Evaluate $\int \dfrac{\ln z}{(1+z)^{2}} d z$
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Evaluate the following integral: $\int \frac{t}{\sqrt{t^{4}-1}} d t$.
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Evaluate the following integral: $\int \frac{t}{\sqrt{t^{4}-1}} d t$. Evaluate the following integral: $\int \dfrac{t}{\sqrt{t^{4}-1}} d t$. Hint: You may use the fact that $\int \sec \theta d \theta=\ln |\sec ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Evaluate the integral $\int_{1}^{2} \dfrac{2 s-2}{\sqrt{-s^{2}+2 s+3}} d s$
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Evaluate $\int \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$
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Determine whether the integral $\int_{0}^{1} \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ is convergent or divergent.
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Evaluate $\int_{-1}^{2} \dfrac{x}{\sqrt{10+2 x+x^{2}}} d x=$
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Evaluate $\int_{-1}^{2} \dfrac{x}{\sqrt{10+2 x+x^{2}}} d x=$Evaluate $\int_{-1}^{2} \dfrac{x}{\sqrt{10+2 x+x^{2}}} d x=$     A. $\quad 3(1-\sqrt{2})-\ln (1+\sqrt{2})$   B. $3(\sqrt{2}-1)-\ln ...
by MathsGee Platinum
(103,030 points)
asked in Mathematics Jan 13
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Evaluate $\int_{1}^{2} \frac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$
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Evaluate $\int_{1}^{2} \frac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$Evaluate $\int_{1}^{2} \dfrac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$   A. $\quad \ln \left(\frac{27}{20}\right)+\arctan 2-\frac{\pi}{4}$ ...
by MathsGee Platinum
(103,030 points)
asked in Mathematics Jan 13
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Evaluate $\int_{0}^{\pi / 4} \sin 3 x \cos 5 x d x=$
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Evaluate $\int_{0}^{\pi / 4} \sin 3 x \cos 5 x d x=$Evaluate $\int_{0}^{\pi / 4} \sin 3 x \cos 5 x d x=$   A. $\frac{1}{2}$   B. $-\frac{1}{2}$   C. $\frac{1}{4}$   D. $-\fra ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Evaluate $\int_{0}^{\infty} \frac{4}{x^{2}+2} d x=$
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Evaluate $\int_{0}^{\infty} \frac{4}{x^{2}+2} d x=$Evaluate $\int_{0}^{\infty} \frac{4}{x^{2}+2} d x=$   A. $-\frac{\pi}{\sqrt{2}}$   B. $\quad \sqrt{2} \pi$   C. $\frac{\pi}{\sqrt ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Find $\frac{d}{d x}\left(x \int_{2}^{x^{2}} \frac{1}{9+t^{2}} d t\right)$
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Determine whether the integral $\int_{3}^{3+e} \ln (x-3) d x$ is convergent or divergent. If convergent, give the value the integral converges to.

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Find the domain, the asymptotes (if any) of $f$ and classify each asymptote as vertical, horizontal or slant.
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Find the domain, the asymptotes (if any) of $f$ and classify each asymptote as vertical, horizontal or slant.Let $$ f(x)=\frac{x^{2}-3}{x+2} $$ You may use that $$ f^{\prime}(x)=\frac{x^{2}+4 x+3}{(x+2)^{2}} \quad \text { and } \quad f^{\prime \prime}(x)=\fra ...
by MathsGee Platinum
(103,030 points)
asked in Mathematics Jan 13
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