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MATH 16A WORKSHEET 5-
(1) Let f(t) = t3(t2 - 1). Find f''(3), df/dt, d2f/dt2|t=1, and d/dt(df/dt).
(2) Let f(x) = x3 - 3x + 2. The slope of the tangent line to f at (2, f(2)) is the same as the slope of the tangent line to f at (a, f(a)), where a ≠ 2. Find a.
(3) Let f(x) = x3 - 3x. Find a linear function (i.e. g(x) = ax + b for some a and b) which passes through (0, f(0)) and has the same slope as the slope of the tangent line to f at (0, f(0)).
(4) Using limits, compute f'(0) where f(x) = √(x2 + 1) at x = 0.
(5) Carefully justify why the function
is differentiable at x = 0.
write the related multiplication or division sentence. draw a quik picture that shows the sentence.
A plane flies 540 miles for 2 hours in the direction of the wind. Then it turns around and flies 690 miles for 3 hours against the same wind. Find the speed of the plane in still air and the wind speed.
If the length of a rectangle is 2 less than 5 times the width and the perimeter is 476", what is the dimension?
Please prove the following theorem: A system of linear equations has zero, one or infinitely many solutions; there are no other possibilities.
Determine the area enclosed between the x-axis and each of the functions below within the specified intervals.
What is the estimated speed of a car that left a skid mark of 110 feet? Round your answer to the nearest mph.
Which of the following sets are linear spaces?
1. what is the simple interest on a 1500 loan at 12 for 2 years?2. what would be the amount of compound interest on
A final exam in Sociology has a mean of 72 and a standard deviation of 9.2. if 35 students are randomly selected, find the probability that the mean of their test scores will be greater than 76.
Consider the intersection of level surfaces of F = x^3 + y^3 - u^3 - v^3 and G = xu + yv.
A cylinder is inscribed in a right circular cone of height 4.5 and radius (at the base) equal to 7.5. What are the dimensions of such a cylinder which has maximum volume?
Determine whether the statements are true or false. Prove the statements which are true; note that Venn Diagrams are not proofs - Determine whether R is reflexive, symmetric, antisymmetric, or transitive.
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