Calculus Answers

Derive the expression for electric potential due a uniformly charged spherical
shell at a point outside the shell.

you have been given the mathematical model to calculate velocity of a car accelerating from rest in straight line: v(t) = A (1-e ^ - t/tmaxspeed) (anything after the symbol ^ is to the power of) v(t is instantaneous velocity of car (m/s), t is time in seconds, tmaxspeed is time to reach maximum speed in seconds and A is constant. you are given the information that t (0-28 m/s) is 2.6s, t (400m) is 10.46s & tmaxspeed is 7s. please derive an equation a(t) for the instantaneous acceleration of the car as a function of time? Identify the acceleration of the car at t = 0s and asymptote of this function as t → ∞?

Trace the curve 3 2 y = x −1 , and state all the properties you use to trace it.

For which values of a and b is the following equation true?

lim (sinx/x³ + a + b/x²) = 0
x - 0

Can the Intermediate Value Theorem be applied to show that there is a root of the
equation X^5 - X³ + 3x - 5 =0 in the given interval [2,1] ? If yes, apply it

Find an expression for the function whose graph consists of the line segment from
the point )2,2 (− to the point )0,1 (− together with the top half of the circle with
centre at the origin and radius 1.

The cost of production of a substance per unit is given by the formula C = q^2 - 4q +1 , where q is the material cost. Find the selling price per unit, so that the profit on 100 units will be Rs.200, if q = 15 . Also calculate the cost of material per unit so that profit of 100 units can be maximized,
if the selling price is Rs. 200.

Obtain the largest possible domain, and corresponding range, of the function f, defined by f(x)=(x-2)/(3-x)

Find the output yielding maximum profit for the cost function
C =0.7 x^3 − 0.8 x^2 + 12x +9
given that the cost price of x is Rs 45/- per unit.

Express the function g: R+-R+ is defined by , g(X) =1/√x+√x, as a composition of three function