A man 2 m high walks at a uniform speed of 5 km/ hr away from a lamp post 6 m high. Find the rate at which the length of his shadow increases?

At what point on the curve y = x² on [-2, 2] is the tangent parallel to X-axis?

Find the maximum and minimum values of f(x) = |x+3| ∀ \(x\in R\).

Find the intervals of increasing and decreasing function for f(x) = x³ + 2x² - 1.

Find x if the rate of decrease of \(\frac { { x }^{ 2 } }{ 2 } -2x+5\) is twice the decrease of x.

Find the point on the parabola y²=18x at which the ordinate increases at twice the rate of the abscissa.

Find the point at which the curve y-e^xy+x=0 has a vertical tangent.

Find the equation of the tangent to the curve y²=4x+5 and which is parallel to y=2x+7

Using Rolle’s theorem find the value of c for f(x) = sin x in[0,2π]

Verify Rolle ’s Theorem for \(f(x)=\left| x-1 \right| ,O\le x\le 2\) 

If f(1)=10 and \(f(x)\ge 2\) for \(1\le x\le 4\) how small can f(4) possible be? 

Verify Lagrange’s Mean Value theorem for \(f(x)=\sqrt { x-2 } \) in the interva [2,6]

Obtain Maclaurin’s Series expansion for e^2x.

Expand the polynomial f(x)=x²-3x+2 in power of (x-2)

Evaluate the following limits, if necessary using L’Hopitalrule
(i) \(\underset { x\rightarrow 2 }{ lim } \cfrac { sin\pi x }{ 2-x } \) 
(ii) \(\cfrac { lim }{ x\rightarrow 2 } \cfrac { { x }^{ n }-{ a }^{ n } }{ x-2 } \) 
(iii) \(\underset { x\rightarrow \infty }{ lim } \cfrac { sin\frac { 2 }{ x } }{ \frac { 1 }{ x } } \)
(iv) \(\underset { x\rightarrow \infty }{ lim } \cfrac { { x }^{ 2 } }{ { e }^{ x } } \)