Chapter 3.2, Problem 68E

Evaluate the following Limits: e6x-1 Lim +0Sin3x 7x-5x2 2x-1+ Cos 4x +6 c) Lim b) Lim + x³-x2 X-0 1-e' 4x d) Lim 6x²-3 X+0 6x+2x² Find the derivatives of the following functions using the Limit definition of derivative

15A cylindrical tank with radius 8 m is being filled with water at a rate of 2 m³/min. What is the rate of change of the water height in this tank? 6)A box with a square base and an open top must box that will minimi

#12 The radius of a sphere increases at a rate of 3 in/sec. How fast is the volume increasing when the diameter is 24

84 256 cubic inches. Find the dimensions of the of material used (the surface area). A farmer wishes to enclose a rectangular plot using 200 m of fencing material. One side of the land borders a river and does not need fencing. What is the largest area that can be enclosed? For the function y=x³-3x²-1, use derivatives to: 3 b) 2x - 6x2 (a) determine the int

Can you solve this 6 questions numerical method and teach me how to solve it and what we use.

9Wire of length 20m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Round your answer to the nearest hundredth.

Use Laplace transform to solve the initial value problem y' + y = tsin(t), y(0) = 0

The function g is defined by g(x) = sec² x + tan x. What are all solutions to g(x) = 1 on the interval 0 ≤ x ≤ 2π ? A x = = 0, x == = 3, x = π, x = 7 4 , 4 and x 2π only = B x = 4' 1, x = 1, x = 57 and x = 3 only C x = πk and x = - +πk D , where is any integer П x = +πk and П x = +πk, where k is any integer

Vector v = PQ has initial point P (2, 14) and terminal point Q (7, 3). Vector v = RS has initial point R (29, 8) and terminal point S (12, 17). Part A: Write u and v in linear form. Show all necessary work. Part B: Write u and v in trigonometric form. Show all necessary work. Part C: Find 7u − 4v. Show all necessary calculations.