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Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 :: Calculus by jthompson85
f(x) = [(2x+4)/(3x-1)]^3
  • f'(x) = 3[(2x+4)/(3x-1)]^2[((3x-1)(2) -(2x+4)(3))/(3x-1)^2]
Grade 12 :: Calculus by jthompson85
f(x) = 5sin(x^2+1)
  • f'(x) = 5cos(x^2+1)(2x)
Grade 12 :: Calculus by jthompson85
f(x) = sqrt (9x^2 +4)
  • f'(x) = (18x)/(2(sqrt(9x^2 + 4)
Grade 12 :: Calculus by cvenable34
Find the limit:
lim(2x^2)/(3x^2+5) as xrarroo
  • 2/3
Grade 12 :: Calculus by jthompson85
f(x) = sqrt tan(3x)
  • f'(x) =1/(2(sqrttan(3x)))(sec^2(3x))(3)
Grade 12 :: Calculus by jthompson85
f(x) = sec(9x^2)
  • f'(x) = sec(9x^2)tan(9x^2)(18x)
Grade 12 :: Calculus by cvenable34
Find the limit:
lim(5cosx)/x as xrarroo
  • 0
Grade 12 :: Calculus by cvenable34
Can the Mean Value Theorem be applied to the function f(x)=1/x^2on 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 jthompson85
f(x) = ln(3x^2 + 9x + 4)
  • f'(x) = 1/(3x^2+9x+4)(6x+9)
Grade 12 :: Calculus by skweckwerth
introot5x^2
Grade 12 :: Calculus by jthompson85
f(x)=2^cosx
  • f'(x) = 2^cosx ln (2) (-sinx)
Grade 12 :: Calculus by skweckwerth
int 1/t^6
Grade 12 :: Calculus by ew609980
int x^2/(x^3+5) dx
  • 1/3 ln(x^3+5)
Grade 12 :: Calculus by cvenable34
Determine the points of inflection of the function:
f(x)=x+cosx, [0,2pi]
  • (π/2, π/2), (3π/2, 3π/2)
Grade 12 :: Calculus by cvenable34
Find the critical numbers (if any) and the open intervals on which the function is increasing or decreasing:
h(x)=sqrt(x)(x-3), x>0
  • Critical number: x=1
    Increasing (-∞, 1), (7/3, ∞)
    Decreasing (1, 7/3)
Grade 12 :: Calculus by cvenable34
Find the absolute extrema of the function on the closed interval:
g(x)=2x+5cosx, [0,2pi]
  • Maximum: (2π, 17.57)
    Minimum: (2.73, 0.88)
Grade 12 :: Calculus by skweckwerth
int(7+3x^(3/2))//2rootx
Grade 12 :: Calculus by ap1111
int_1^oo x^3 dx
  • True
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