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Find derivatives of using multiple formulae

Simplify: 3n−6m218m−3n−5\frac{3n^{-6}m^{2}}{18m^{-3}n^{-5}}
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Version B\newline77. Solve \newline△ABC\triangle ABC using the diagram and the given measurements. (The triangle is not drawn to scale.) Round answers to the nearest tenth. \newlineA=44∘A=44^\circ, a=7a=7\newline88. Find one positive angle and one negative angle that is coterminal with \newline−118∘-118^\circ.\newline(11 pt each)\newlinePositive Angle: \newline\quad Negative Angle: \newline\quad\newline99. Which pair of angles is coterminal?\newline\quad ( 22 pts)\newlineA. \newline30∘\quad30^\circ and \newline−30∘-30^\circ\newlineC. \newline−330∘\quad-330^\circ and \newline−30∘-30^\circ\newlineB. \newline30∘\quad30^\circ and \newlineA=44∘A=44^\circ22\newlineD. None of the Above\newline1010. Convert \newlineA=44∘A=44^\circ33 to radians.\newline\quad (22pts)\newlineA. \newlineA=44∘A=44^\circ55\newlineC. \newlineA=44∘A=44^\circ66\newlineB.\newlineA=44∘A=44^\circ77\newlineD.\newlineA=44∘A=44^\circ88
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UNIVERSITY OF THEPUNJAB\newlineB.S. 44 Years Program / First Semester-Fall 20222022\newlineRoll N\newlineRoll.....\newlineTime: 33\newlineCalculus - 11\newlineCourse Code: MATH−1001-1001\newlineTHE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDE\newlineQ.11. Solve the following:\newline(66\times55=3030)\newline\newline(i)\newlineReplace the polar equation by equivalent Cartesian equations, and identify the\newlinegraphs. \newliner=42cos⁡θ−sin⁡θr=\frac{4}{2\cos \theta-\sin \theta}\newline\newline(ii)\newlineEvaluate the integral \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?\newline\newline(iii)\newlineFind the values of \newlinexx for which \newlinef(x)f(x) is continuous: \newlinef(x)=x4+205x(x−2)f(x)=\frac{x^{4}+20}{5x(x-2)}.\newline\newline(iv)\newlineFind derivative of \newlinef(x)f(x) if \newlinef(x)=(sin⁡x1+cos⁡x)2f(x)=\left(\frac{\sin x}{1+\cos x}\right)^{2}.\newline\newline(v)\newlineSolve : \newlinelim⁡x→0(1sin⁡x−1x)\lim_{x \to 0}\left(\frac{1}{\sin x}-\frac{1}{x}\right).\newline\newline(vi)\newlineFind \newlinedydx\frac{dy}{dx} if \newliney=∫1x2cos⁡tdty=\int_{1}^{x^{2}}\cos tdt.\newline\newlineSolve the following:\newline(55\times66=3030)\newline\newlineQ. 22\newlineEvaluate the integral \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?00.\newlineQ. 33\newlineFind the intervals on which the function \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?11 is increasing and decreasing\newlineQ. 44\newlineFind the area enclosed by parabola \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?22 and the line \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?33.\newlineQ. 55\newlineFind \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?44 of \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?55.\newlineQ. 66\newlineSolve the integral \newline∫r21−t2dr=?\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?66.
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UNIVERSITY OF THEPUNJAB\newlineB.S. 44 Years Program / First Semester-Fall 20222022\newlineRoll N\newlineRoll\newlineTime: 33\newlineCalculus - 11\newlineCourse Code: MATH−1001-1001\newlineTHE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDEI\newlineQ.11. Solve the following:\newline(6×5=30) (6 \times 5=30) \newline\begin{tabular}{|l|l|}\newline\hline (i) & \begin{tabular}{l} \newlineReplace the polar equation by equivalent Cartesian equations, and identify the \\\newlinegraphs. r=42cos⁡θ−sin⁡θ \mathrm{r}=\frac{4}{2 \cos \theta-\sin \theta} \newline\end{tabular} \\\newline\hline (ii) & Evaluate the integral ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? \\\newline\hline (iii) & Find the values of x \mathrm{x} for which f(x) \mathrm{f}(\mathrm{x}) is continuous: f(x)=x4+205x(x−2) f(x)=\frac{x^{4}+20}{5 x(x-2)} . \\\newline\hline (iv) & Find derivative of f(x) \mathrm{f}(\mathrm{x}) if :f(x)=(sin⁡x1+cos⁡x)2 : f(x)=\left(\frac{\sin x}{1+\cos x}\right)^{2} . \\\newline\hline (v) & Solve: lim⁡x→0(1sin⁡x−1x) \lim _{x \rightarrow 0}\left(\frac{1}{\sin x}-\frac{1}{x}\right) . \\\newline\hline (vi) & Find dydx \frac{d y}{d x} if y=∫1x2cos⁡tdt y=\int_{1}^{x^{2}} \cos t d t . \\\newline\hline\newline\end{tabular}\newlineSolve the following:\newline∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 00\newline\begin{tabular}{|l|l|}\newline\hline Q. 22 & Evaluate the integral ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 11. \\\newline\hline Q. 33 & Find the intervals on which the function ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 22 is increasing and decreasing. \\\newline\hline Q. 44 & Find the area enclosed by parabola ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 33 and the line ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 44. \\\newline\hline Q. 55 & Find ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 55 of ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 66. \\\newline\hline Q. 66 & Solve the integral ∫r21−r2dr=? \int \frac{r^{2}}{\sqrt{1-r^{2}}} d r=? 77. \\\newline\hline\newline\end{tabular}
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