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Solve the following:$\newline$$(6\times5=30)$$\newline$i) Find the domain and range of the function $\newline$$f(x)=\sqrt{1-x^{2}}$ Page $47$$\newline$(ii) Prove that If $\newline$$f$ is differentiable at a point $\newline$$a$ in $\text{Dom} f$, then $\newline$$f$ is continuous at $\newline$$a$$\newline$(ii) Show that polar coordinates $\newline$$P(3,0)$ and $\newline$$Q(-3,\pi)$ represent the same point.$\newline$iv) Evaluate $\newline$$\int\frac{dx}{x^{2}+3x+4}$$\newline$v) Find point of Inflection of the curve $\newline$$f(x)=\sqrt{1-x^{2}}$$0$ unit $47$ e, $\newline$$f(x)=\sqrt{1-x^{2}}$$1$$\newline$-vi) Find area of the region bounded by $\newline$$f(x)=\sqrt{1-x^{2}}$$2$, x-axis, $f(x)=\sqrt{1-x^{2}}$$3$, $f(x)=\sqrt{1-x^{2}}$$4$$\newline$Q.$2$. Solve the following:$\newline$$f(x)=\sqrt{1-x^{2}}$$5$$\newline$H Examine the continuity of $\newline$$f(x)=\sqrt{1-x^{2}}$$6$ at $\newline$$f(x)=\sqrt{1-x^{2}}$$7$ where $\newline$$f(x)=\sqrt{1-x^{2}}$$8$$\newline$ii) Evaluate $\newline$$f(x)=\sqrt{1-x^{2}}$$9$$\newline$(iii) Find the area enclosed by the graph of the circle of radius $\newline$$f$$0$.$\newline$iv) Find reduction formula for $\newline$$f$$1$ and hence find $\newline$$f$$2$$\newline$v) By using substitution $\newline$$f$$3$ show that $\newline$$f$$4$