Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2. If y = tan-1(x/y), find the approximate change in u as x changes from 10 to 10.02 and y changes from 4 to 4.01. How fast is the surface area increasing when the length of each edge is 12 cm? a. The volume of a cube is increasing at the rate of 6 cm3/min. If y = +, find x for which dy/dx = 0 2 4 a. Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. Find two numbers whose sum is 8 if the product of one number and the cube of the other is a maximum. Find the point on the curve y = x3 – 3x for which the tangent line is parallel to the x axis. Find the radius of curvature of y = x3 at the point (1, 1). At what rate is the tip of his shadow moving if the man is 2 m tall? a. A man is walking at the rate of 1.5 m/s toward a street light which is 5 m above the level ground. Find the value of x for which y = x5 – 5x3 – 20x – 2 qill have a maximum point. Find the approximate surface area of a sphere of radius 5.02 cm. Calculate its velocity when it strikes the ground. The height s of the ball above the roof is given by the equation s = 96t – 16t2 where s is measured in ft and the time t in sec. A ball is thrown vertically upward from a roof 112 ft above the ground. If z = xy2, and x changes from 1 to 1.01, and y changes from 2 to 1.98, find the approximate change in z. Find the angle of intersection between the curves y = x2 and x = y2. Find the value of x fro which y = x3 – 3x2 has a minimum value. The tangent line to the curve y = x3 at the point (1, 1) will intersect the x axis at x = a. If xy + x y = 2, find dy/dx at the point (1, 1). If f(x) = tanx – x and g(x) = x, evaluate the limit of f(x)/g(x) as x approaches zero. How fast does the diagonal of a cube increase if each edge of the cube increases at a constant rate of 5 cm/s? a. For what value of x will the curve y = x – 3x + 4 be concave upward? a. Find the derivative of y with respect to x of y = xInx – x. If an error of 1 percent is made in measuring the edge of a cube, what is the approximate percentage error in the compute volume? a. Find the slope of y = 1 – x at the point where y = 9. How fast is the area changing when R = 4 cm? a. The radius R of a circle is increasing at the rate of 1 cm per sec. If y = x – 2x and x changes from 2 to 2.01, find y a. If y = x3 – 2x2 + 3x – 1, then d2y/dx2 is equal to 17. If y = sin2x, the derivative dy/dx is equal to a. The slope of the tangent to y = 2 – x2 at the point (1, 1) is a. Find x for which of the line tangent to the parabola y = 4x – x2 is horizontal. Find the velocity of the particle when t = 2. The motion of a particle along the x axis is given by the equation x = 2t3 – 3t2. undefined f ( x) if f(x) = x – 2 and g(x) = x2 – 1. Which of the following no horizontal asymptote? x2 x3 x2 x3 a. What is the 50 derivative of y = cosx? a. If N(x) = sinx – sinθ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. If f(x) = Inx and g(x) = logx and if g(x) = kf(x), find k. At what point of the curve y = x3 + 3x are the values of y’ and y” equal? a. The rate of change of the area of a circle with respect to its radius when the diameter is 6 cm is a. Evaluate the limit of In(1 – x)/x as x approaches zero. Find the slope of the line tangent to y = 4/x at x = 2. The function f ( x) = 2 is discontinuous at x = x − 2x − 3 a. If f(x) = e-x + 1, then f’(1) is equal to a. Find the rate of change of the volume of a cube with respect to its side when the side is 6 cm? a. EXAMINATION IN DIFFERENTIAL CALCULUS ENCIRCLE THE LETTER OF THE CORRECT ANSWER.
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