Could you please help me with these questions?

1. Compute the following limits: (a) lim COs x - cos (3x) (b) lim 22 x-+0o Vatvx- Vx) , (c) lim x2 sin(!) x+0 2. Let 3x2 - 1, if x 1. Determine the values of c and d, such that f(x) is continuous everywhere. 3. Which of the following functions is differentiable at x = 0? f(x) = xx, g(x) = xval, h(x) = x+lal, j(x) = asin (2), ifx # 0, if x = 0. 4. Find derivatives of the following functions: (a) tan vi, (b) 1 - x2 1 + x2: (c) In(csc x + cot x), (d) (cosh x)*, (e) tan-1 2 (f) sin a sin 5. Find the tangent line of the curve xy + Iny = 1 at the point (1, 1). 2t+t2 6. Find the tangent line of the curve 1+ +3 , y = 2t-t2 at the point when t = 1. 1+ + 3 , 7. A stone thrown into a still pond produces concentric circular ripples. If the radius of the largest ripple increases at the rate of 0.60 meters per second, how fast is the area within this ripple increasing when the radius is 50 meters