Questions from General Calculus

Q: If f is differentiable at a, where a > 0,

If f is differentiable at a, where a > 0, evaluate the following limit in terms of f'(a):

Q: Find a cubic function y = ax2 + bx2 + cx +

Find a cubic function y = ax2 + bx2 + cx + d whose graph has horizontal tangents at the points (-2, 6) and (2, 6).

Q: Find all values of a such that f is continuous on R

Find all values of a such that f is continuous on R:

Q: Tangent lines T1 and T2 are drawn at two points P1 and

Tangent lines T1 and T2 are drawn at two points P1 and P2 on the parabola y = x2 and they intersect at a point P. Another tangent line T is drawn at a point between P1 and P2; it intersects T1 at Q1 a...

Q: Show that dn/dxn = eax sin bx) = rneaxs

Show that dn/dxn = eax sin bx) = rneaxs sin (bx + nθ) where a and b are positive numbers, r2 = a2 + b2, and θ = tan-1(b/a).

Q: Find the values of the constants a and b such that limx

Find the values of the constants a and b such that limx→0 3√ax + b – 2/x = 5/12

Q: If [[x]] denotes the greatest integer function, find limx

If [[x]] denotes the greatest integer function, find limx→∞ x/[[x]].

Q: If f and g are differentiable functions with f (0)

If f and g are differentiable functions with f (0) = g (0) = 0 and g'(0) ≠ 0, show that

Q: If y = ((x/√a2 – 1) – (

If y = ((x/√a2 – 1) – (2/√a2 – 1) arctan sin x/a + (√a2 – 1) + cos x) show that y' = 1/a + cos x.

Q: For what value of does the equation e2x = k√x

For what value of does the equation e2x = k√x have exactly one solution?