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Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 :: Calculus by jthompson85
[math]f(x) = [(2x+4)/(3x-1)]^3[/math]
  • [math]f'(x) = 3[(2x+4)/(3x-1)]^2[((3x-1)(2) -(2x+4)(3))/(3x-1)^2][/math]
Grade 12 :: Calculus by jthompson85
[math]f(x) = 5sin(x^2+1)[/math]
  • [math]f'(x) = 5cos(x^2+1)(2x)[/math]
Grade 12 :: Calculus by jthompson85
[math]f(x) = sqrt (9x^2 +4)[/math]
  • [math]f'(x) = (18x)/(2(sqrt(9x^2 + 4)[/math]
Grade 12 :: Calculus by jthompson85
[math]f(x) = sqrt tan(3x)[/math]
  • [math]f'(x) =1/(2(sqrttan(3x)))(sec^2(3x))(3)[/math]
Grade 12 :: Calculus by jthompson85
[math]f(x) = sec(9x^2)[/math]
  • [math]f'(x) = sec(9x^2)tan(9x^2)(18x)[/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 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 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)
Grade 12 :: Calculus by jthompson85
[math]f(x)=2^cosx[/math]
  • [math]f'(x) = 2^cosx ln (2) (-sinx)[/math]
Grade 12 :: Calculus by cvenable34
Determine the points of inflection of the function:
[math]f(x)=x+cosx, [0,2pi][/math]
  • (π/2, π/2), (3π/2, 3π/2)
Grade 12 :: Calculus by ap1111
[math]int_1^oo x^3 dx[/math]
  • True
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