Review Problems Chapter 5.1 – 5.7

Review Problems Find the domain of the function: f(x) = ln(3x + 1).

Review Problems Find the domain of the function: f(x) = 3 + ln(x - 1). (1, )

Review Problems Match the graph with the correct function [A] f(x) = ln x [B] f(x) = ex-1 [C] f(x) = ln(x - 1) [D] f(x) = ex Review Problems Match the graph with the correct function [A] f(x) = ln x   [B] f(x) = ex-1 [C] f(x) = ln(x - 1) [D] f(x) = ex

Review Problems Sketch the graph: f(x) = ln|x|.

Review Problems Solve for x: ln(5x + 1) + ln x = ln 4

Review Problems Solve for x: ln(5x - 1) - ln x = 3.

Review Problems dy/dx for y = ln(5 - x)6

Review Problems Find the derivative: f(x) = ln(x3 + 3x)3

Review Problems Find the derivative:

Review Problems Find the derivative:

Review Problems Find the derivative:

Review Problems Differentiate: y = ln(ln tan x)

Review Problems Find y’ y = ln|2x2 - 5|

Review Problems Find y’ if ln xy = x + y

Review Problems Use logarithmic differentiation to find

Review Problems Find the slope of the tangent line to the graph of y = ln x2 at the point where x = e2

Review Problems Evaluate the integral: ln 4

Review Problems Evaluate the integral: ln|ax + b| + C

Review Problems Evaluate the integral: -2

Review Problems Evaluate the integral:

Review Problems Evaluate the integral: x + ln(x2 + 1) + C x +

Review Problems Evaluate the integral: 8x + ln(x2 + 1) + C

Review Problems Evaluate the integral: 9x - ln(x2 + 1) + C

Review Problems Evaluate the integral: + C

Review Problems ln|sec 3x| + C Evaluate the integral: ln|sec 3x| + C

Review Problems Evaluate the integral: -2 cos x + ln|csc x + cot x| + C

Review Problems Evaluate the integral: ln|tan x| + C

Review Problems Evaluate the integral:

Review Problems Match the graph shown with the correct function [A] f(x) = e (x-1)   [B] f(x) = e-(x-1) [C] f(x) = ex + 1 [D] f(x) = e-x + 1

Review Problems Differentiate:

Review Problems Differentiate:

Review Problems Differentiate:

Review Problems Find: if xey + 1 = xy

Review Problems Find the slope of the tangent line to the graph of y = (ln x)ex at the point where x = 2

Review Problems Evaluate the integral: -ecosx + C

Review Problems Evaluate the integral: + C

Review Problems Evaluate the integral: -95 e-t/5 + C

Review Problems Evaluate the integral: + C

Review Problems Find if y = 3xx3 3xx2[3 + (ln 3)x]

Review Problems Differentiate: y = x1-x x1-x

Review Problems Differentiate y = xx xx[1 + ln x]

Review Problems Evaluate the integral: + C

Review Problems Find the area bounded by the function f(x) = 2-x, the x-axis, x = -2, and x = 1

Review Problems A certain type of bacteria increases continuously at a rate proportional to the number present. If there are 500 present at a given time and 1000 present 2 hours later, how many will there be 5 hours from the initial time given? 2828

Review Problems A certain type of bacteria increases continuously at a rate proportional to the number present. If there are 500 present at a given time and 1000 present 2 hours later, how many hours (from the initial given time) will it take for the numbers to be 2500? Round your answer to 2 decimal places. 4.64

Review Problems A mold culture doubles its mass every three days. Find the growth model for a plate seeded with 1.6 grams of mold. [Hint: Use the model y = Cekt where t is time in days and y is grams of mold.] 1.6e0.23105t

Review Problems The balance in an account triples in 21 years. Assuming that interest is compounded continuously, what is the annual percentage rate? 5.23%

Review Problems The balance in an account triples in 20 years. Assuming that interest is compounded continuously, what is the annual percentage rate? 5.49%

Review Problems A radioactive element has a half-life of 50 days. What percentage of the original sample is left after 85 days? 30.78%

Review Problems A radioactive element has a half-life of 40 days. What percentage of the original sample is left after 48 days? 43.53%

Review Problems y = 10eln(12/5)t/6 The number of fruit flies increases according to the law of exponential growth. If initially there are 10 fruit flies and after 6 hours there are 24, find the number of fruit flies after t hours. y = 10eln(12/5)t/6

Determine whether the function y = 2cos x is a solution to the differential equation Review Problems Determine whether the function y = 2cos x is a solution to the differential equation No

Review Problems verify that is a solution to the differential equation

Review Problems Find the particular solution to the differential equation given the general solution and the initial condition y = 1 - cos x

Review Problems Find the particular solution to the differential equation given the general solution and the initial condition y(0) = 5.

Review Problems Use integration to find a general solution to the differential equation y = (x + 1)3/2 + C

Review Problems Use integration to find a general solution to the differential equation y = 3 ln|1 + x| + C

Review Problems Use integration to find a general solution to the differential equation y=

Review Problems Find the general solution to the first-order differential equation: (4 - x)dy + 2y dx = 0 y = C(4 - x)2

Review Problems Find the general solution to the first-order differential equation: x cos2y + tan y = 0 x2 + sec2y = C

Review Problems Find the general solution to the first-order differential equation: y dx + (y - x)dy = 0 y ln|y| + x = Cy

Review Problems Find the general solution to the first-order differential equation: y=

Review Problems Find the general solution to the first-order differential equation:

Review Problems Find the particular solution of the differential equation that satisfies the initial condition y(0) = 7 y = 500 - 493e-x

Review Problems Find the solution to the initial value problem y(-1) = 0 ey + sin y = (x2 + 1)

Review Problems Find the solution to the initial value problem y(1) = 0 ln(1 + y2) = 2 ln x + x2 - 1