What is true if \( f(x) \) is continuous at \( x=4 \) and \( f(4)=3 ? \)

(iv) Find the equation of the tangent to the conne \( y=x^{3}-x \) at \( x=2 \) v) Evaluate: \( \lim _{x \rightarrow \infty}\left(x-\sqrt{x^{2}+2 x}\right) \) 3. Answen any three of the following quortisy 1) Show that \( f: R \geqslant[4, w] \) given by \( [3 \times 3=9 \) \( f(x)=x^{2}+4 \) 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: \( \lim _{x \rightarrow 1}(2-x)^{\operatorname{cosec} \pi x} \) 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

\( y ^ { \prime \prime } + 4 y = 0 \quad y ( 0 ) = 1 \quad y ^ { \prime } ( 0 ) = 1 \)

\( y ^ { \prime } ( t ) + 2 y + \int _ { 0 } ^ { t } y ( x ) d x \quad y ( 0 ) = 1 \)

\( y ^ { \prime } ( t ) + 2 y + \int _ { 0 } ^ { t } y ( x ) d x \quad y ( 0 ) = 1 \)

\( y ^ { \prime \prime } - y ^ { \prime } - 6 y = 0 \quad y ( 0 ) = 1 \quad y ^ { \prime } ( 0 ) = 2 \)