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A ball thrown straight up is located s feet above the ground at t seconds after it is thrown in accordance with the formula s= 112t-16 t^2. Find a formula for the velocity of the ball and find (a) the time required to reach its highest point, (b) the distance of the highest point above the ground, and (c) the acceleration of the ball at this point.
A ball rolling down an incline travels s feet in t seconds, where s= 5t^2. Derive a formula for the velocity of the ball at time t= t0. How fast is it going (a) after 2 seconds (b) after it has rolled 80 feet?
Find the derivative of the function f(x)=√x with respect to x at x0.
Find the rate of change of the function f(x)= x^3 with respect to x at x0.
1. Write
(2−i) (4−3i)2
3+2i
(4)
in the form a+bi, where a,b ∈ R.
Evaluate ∫C (x + 2y) ds, where C is the curve defined by y = √(4 − x2), for x ∈ [0, 1].
A firm has the following average cost function:
AC = 50+10/Q
(a) Show by differentiation that AC decreases indefinitely as Q
increases. Give an economic interpretation of this phenomenon
(b) Write down the equation for total cost. Hence, write down the
equation for total variable cost and average variable costs. State the
value of fixed costs.
(c) Write down the equation for marginal costs. Comment on the
relationship between TC and MC in this example.
dy/dx + 4y= 8
Find the maximum possible domain and the corresponding range of the quotient functionf/g
where R → R:f are defined by f(X,y)=4xy and g(X,y)= x3+y3
Evaluate the integral "\\int_0^2 e^{x^3}x^2dx".
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