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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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College :: Calculus by as_km
Solve:
int_0^1dx/(1+k^3/x^3)
Grade 11 :: Calculus by jthompson85
f(x)=ln(x^3)
  • f'(x)=1/x^3(3x^2)
College :: Calculus by megomatic
Find lim_(x->oo) (3x^4-8x^2+2)/(7x^4)
College :: Initial Value Problems by BacMan
Solve y''=12x^2 where y'(0) = 15 and y(0) = 13
  • Itegrate:
    y' = int12x^2dx = 4x^3 + c_1

    Using the first condition y'(0) = 15:
    4(0)^3 + c_1 = 15
    c_1 = 15

    Therefore, the differential equation is:
    y' = 4x^3 + 15

    Integrate again:
    y = int(4x^3 + 15)dx = x^4 + 15x + c_2

    Using the second condition y(0) = 13:
    0^4 + 15*0 + c_2 = 13
    c_2 = 13

    The answer is:
    y = x^4 + 15x + 13
Grade 12 :: Calculus by cvenable34
Find the limit:
lim(5cosx)/x as xrarroo
  • 0
Grade 12 :: Calculus by jthompson85
f(x) = ln(3x^2 + 9x + 4)
  • f'(x) = 1/(3x^2+9x+4)(6x+9)
Grade 11 :: Calculus by jthompson85
f(x)=sin^4(cosx^2)
  • f'(x)=4(sin^3(cosx^2))(cos(cosx^2))(-sinx^2)(2x
Grade 12 :: Calculus by ew609980
int x^2/(x^3+5) dx
  • 1/3 ln(x^3+5)
Grade 12 :: Calculus by skweckwerth
int 1/t^6
Grade 12 :: Calculus by skweckwerth
introot5x^2
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 jthompson85
f(x)=2^cosx
  • f'(x) = 2^cosx ln (2) (-sinx)
Grade 11 :: Calculus by jthompson85
f(x)=(sin(4x^2+2x-1))(cos(7x))
  • f'(x)=sin(4x^2 + 2x - 2)(-sin(7x)(7)) + cos(7x)(cos(4x^2+2x - 1)(8x + 2))
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