(iv) Find the equation of the tangent to the conne $$ y=x^{3}-x $$ at $$ x=2 $$ v) Evaluate: $$ \lim _{x ightarrow \infty}\left(x-\sqrt{x^{2}+2 x} ight) $$ 3. Answen any three of the following quortisy 1) Show that $$ f: R \geqslant[4, w] $$ given by $$ [3 imes 3=9 $$ $$ f(x)=x^{2}+4 $$ is invontible. Find $$ f^{\prime} $$ 1) Show that the line $$ y=m v+c $$ touchos the parabula $$ y^{2}=4 a x $$ if $$ c=\frac{a}{m} $$ iii) Find the equation et all lines having slope 2 and being tangent to the curve $$ y+\frac{2}{x-b}=0 $$ iv) Evaluate: $$ \lim _{x ightarrow 1}(2-x)^{\operatorname{cosec} \pi x} $$ v) Formulate the following L.P.P. A porron having a capital of ks. 5000 has to buy tho tyres of bores of toys viz type-1 and type 11 at $$ R_{S} 10 $$ and $$ R_{s} .20 $$ pen box respectively. and sale thom at Rs. 14 and Rs. 25 pen box cospertingly. For reegons of limit on sale he

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(iv) Find the equation of the tangent to the conne $$ y=x^{3}-x $$ at $$ x=2 $$ v) Evaluate: $$ \lim _{x ightarrow \infty}\left(x-\sqrt{x^{2}+2 x}ight) $$ 3. Answen any three of the following quortisy 1) Show that $$ f: R \geqslant[4, w] $$ given by $$ [3 	imes 3=9 $$ $$ f(x)=x^{2}+4 $$ is invontible. Find $$ f^{\prime} $$ 1) Show that the line $$ y=m v+c $$ touchos the parabula $$ y^{2}=4 a x $$ if $$ c=\frac{a}{m} $$ iii) Find the equation et all lines having slope 2 and being tangent to the curve $$ y+\frac{2}{x-b}=0 $$ iv) Evaluate: $$ \lim _{x ightarrow 1}(2-x)^{\operatorname{cosec} \pi x} $$ v) Formulate the following L.P.P. A porron having a capital of ks. 5000 has to buy tho tyres of bores of toys viz type-1 and type 11 at $$ R_{S} 10 $$ and $$ R_{s} .20 $$ pen box respectively. and sale thom at Rs. 14 and Rs. 25 pen box cospertingly. For reegons of limit on sale he

Whittaker Stewart · Accepted Answer

The tangent to the curve $$ y = x^3 - x $$ at $$ x = 2 $$ is $$ y = 11x - 16 $$. The limit $$ \lim_{x \rightarrow \infty} \left( x - \sqrt{x^2 + 2x} \right) $$ equals -1.

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