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limits
derivatives
integrals
integral problems
trig derivatives
100
lim 5 x→−1
5
100
What is the difference quotient equation?
f(x+h)-f(x)/h
100
what are the 4 types of riemann sums?
right, left, midpoint, and trapezoid
100
∫2x^2-4x+13 dx
2/3x^3 - 2x^2 + 13x + C
100
derivative of sin(x)
cos(x)
200
lim -(2x+4)^1/2 x→5/2
-3
200
derivative of 8x^3 + 6x^2 + x + 7
24x^2 + 12x + 1
200
what is an integral?
Area under the curve of a function or Antidervative
200
Integrate ∫x(e^3x)dx
1/3(xe^3x) - 1/9(e^3x) + C
200
derivative of sec(x)
sec(x)tan(x)
300
lim x^3/4x^2+3 x→ ∞
∞
300
derivative of (2x^3+3)/(x+1)
4x^3-3/(x+1)^2
300
Would you use substitution or integration by parts for this integral? ∫0/2 xe^x dx
U substitution
300
Solve the initial value problem. dy/dx=cos(x) + sin(x) y(1)=π(pi)
y=sin(x) - cos(x)
300
derivative of cot^-1(x)
-1/(x^2+1)
400
lim sin(5x)/3x x→0
5/3
400
what is the derivative of a^x
a^x(ln(a))
400
What does LIPET stand for and when do you use it?
Logs|Inverse trig functions|Polynomials|Exponents|Trig: Determines which part of the integral is "u" when integrating by parts.
400
Find the area between y=x^2 + 5x and y=3-x^2. (calculator)
14.29 Units^2
400
derivative of tan(5x)
5sec^2(5x)
500
lim 2tan (2x) x→3π/4+
−∞
500
derivative of sin(x)/x
1
500
what is simpson's rule? (the formula or an explanation)
Area=∫f(x)dx≈(Δx/3)(y0+4y1+2y2+4y3 +2y4…+4yn−1+yn​​) or A riemann sum using parabolic curves instead of rectangular or trapezoidal approximations.
500
Determine the volume of the solid obtained by rotating the region bounded by y=x^2 - 4x + 5, x+1, x=4, and the x-axis about the x-axis. (calculator)
78π(pi)/5
500
This is the derivative of what function? cos(x)/(x^2+1)
tan^-1(sin(x))