Clac Ch. 5-7 Review

7 ln(|x-7|) + C

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) INDEF. SYMBOL 7/x-7 dx

ln(|x^9+2x|) + C

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) INDEF. SYMBOL 9x^8 + 2/x^9 + 2x dx

C - ln(|6-x^5|)/5

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) INDEF. SYMBOL x^4/6-x^5 dx

1/2 ln (x-12) - (1/2) ln (x)

Properties of logarithms - expand ln (the square root of x-12/x)

ln(x) - ln(54)

Properties of logarithms - expand ln(x/54)

1/2x ln (x-7)

Properties of logarithms - expand x ln (the square root of x-7)

(2/square root of e, -6/e) and (2/e^3/2, -18/e^3)

Rel. Extremum and ppi: y = 3x^2 ln(x/2) Relative Extrema = ( , ) ppi:

(1/2,1) and DNE

Rel. Extremum and ppi: y=2x-ln(2x) Relative Extrema = ( , ) ppi:

(4/square root of e, -40/e) and (4/e^(3/2), -120/e^3)

Rel. Extremum and ppi: y=5x^2 ln(x/4) Relative Extrema = ( , ) ppi:

(1/9,1) and DNE

Rel. Extremum and ppi: y=9x-ln(9x) Relative Extrema = ( , ) ppi:

y=7x-7

Find an equation of the tangent line to the graph of the logarithmic function at the point (1,0). y=ln(x^7)

5(2x ln(5x) +x)

Find the derivative: f(x)=5x^2 ln(5x)

8(2x ln(8x) +x)

Find the derivative: f(x)=8x^2 ln(8x)

5/x(x+5)

Find the derivative: f(x)=ln (2x/x+5)

1/x

Find the derivative: f(x)=ln(5x)

-3/x^2-9

Find the derivative: y=ln (square root of x+3/x-3)

-9cot (9x)

Find the derivative: y=ln (|csc(9x)|)

ln(|x^3+18x^2+15x+4|)/3 + C

Find the indefinite integral. INDEF. SYMBOL x^2 +12x +5/x^3+18x^2+15x+4 dx

(-infinity,4), 4, and (3,0)

Find the domain, vertical asymptote, and x-intercept of the logarithmic function. (Enter your domain using interval notation.) f(x) = ln(4 − x) Domain: ( , ) VA: x= x-int:

2(x^2+2)/(x-1)^2 (x+2)^2

Use logarithmic differentiation to solve: y= (x+1)(x-2)/(x-1)(x+2), x>2

8(x^2+8)/(x-1)^2 (x+8)^2

Use logarithmic differentiation to solve: y= (x+1)(x-8)/(x-1)(x+8), x>8

200x/(x^2+100)^(3/2) (x^2-100)^(1/2)

Use logarithmic differentiation to solve: y= square root of x^2-100/x^2+100, x > 10

162x/(x^2+81)^(3/2) (x^2-81)^(1/2)

Use logarithmic differentiation to solve: y= square root of x^2-81/x^2+81, x > 9