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UNIVERSITY OF THEPUNJAB$\newline$B.S. $4$ Years Program / First Semester-Fall $2022$$\newline$Roll N$\newline$Roll.....$\newline$Time: $3$$\newline$Calculus - $1$$\newline$Course Code: MATH$-1001$$\newline$THE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDE$\newline$Q.$1$. Solve the following:$\newline$($6$\times$5$=$30$)$\newline$$\newline$(i)$\newline$Replace the polar equation by equivalent Cartesian equations, and identify the$\newline$graphs. $\newline$$$r=\frac{4}{2\cos \theta-\sin \theta}$$$\newline$$\newline$(ii)$\newline$Evaluate the integral $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$\newline$$\newline$(iii)$\newline$Find the values of $\newline$$$x$$ for which $\newline$$$f(x)$$ is continuous: $\newline$$$f(x)=\frac{x^{4}+20}{5x(x-2)}$$.$\newline$$\newline$(iv)$\newline$Find derivative of $\newline$$$f(x)$$ if $\newline$$$f(x)=\left(\frac{\sin x}{1+\cos x}\right)^{2}$$.$\newline$$\newline$(v)$\newline$Solve : $\newline$$$\lim_{x \to 0}\left(\frac{1}{\sin x}-\frac{1}{x}\right)$$.$\newline$$\newline$(vi)$\newline$Find $\newline$$$\frac{dy}{dx}$$ if $\newline$$$y=\int_{1}^{x^{2}}\cos tdt$$.$\newline$$\newline$Solve the following:$\newline$($5$\times$6$=$30$)$\newline$$\newline$Q. $2$$\newline$Evaluate the integral $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$0$.$\newline$Q. $3$$\newline$Find the intervals on which the function $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$1$ is increasing and decreasing$\newline$Q. $4$$\newline$Find the area enclosed by parabola $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$2$ and the line $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$3$.$\newline$Q. $5$$\newline$Find $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$4$ of $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$5$.$\newline$Q. $6$$\newline$Solve the integral $\newline$$$\int\frac{r^{2}}{\sqrt{1-t^{2}}}dr=?$$$6$.