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Calculus Questions - All Grades

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The Calculus questions below are in the following grade levels:
Grades: 11 12 College
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Grade 12 :: Calculus by jthompson85
[math]f(x) = sec(9x^2)[/math]
  • [math]f'(x) = sec(9x^2)tan(9x^2)(18x)[/math]
Grade 11 :: Calculus by jthompson85
[math]f(x) = e^(5x^2 - 3x + 2)[/math]
  • [math]f'(x)=e^(5x^2-3x+2)(10x-3)[/math]
Grade 11 :: Calculus by jthompson85
[math]f(x)=ln(x^3)[/math]
  • [math]f'(x)=1/x^3(3x^2)[/math]
Grade 12 :: Calculus by ew609980
[math]int x^2/(x^3+5) dx[/math]
  • [math]1/3 ln(x^3+5)[/math]
Grade 12 :: Calculus by jthompson85
[math]f(x) = ln(3x^2 + 9x + 4)[/math]
  • [math]f'(x) = 1/(3x^2+9x+4)(6x+9)[/math]
Grade 12 :: Calculus by cvenable34
Can the Mean Value Theorem be applied to the function [math]f(x)=1/x^2[/math]on the interval [-2, 1]? Explain why or why not.
  • No. There is a nonremovable discontinuity for f(x) in that interval.
Grade 12 :: Calculus by skweckwerth
[math]introot5x^2[/math]
Grade 12 :: Calculus by skweckwerth
[math]int 1/t^6[/math]
Grade 11 :: Calculus by jthompson85
[math]f(x)=sin^4(cosx^2)[/math]
  • [math]f'(x)=4(sin^3(cosx^2))(cos(cosx^2))(-sinx^2)(2x[/math]
Grade 12 :: Calculus by cvenable34
Find the critical numbers (if any) and the open intervals on which the function is increasing or decreasing:
[math]h(x)=sqrt(x)(x-3), x>0[/math]
  • Critical number: x=1
    Increasing (-∞, 1), (7/3, ∞)
    Decreasing (1, 7/3)
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