What is the Completed Fundamental Theorem of Calculus
∫ab f(x)dx=?
∫ab f(x)dx= _F(b)-F(a)_
100
What is the difference between average and instantaneous velocity?
Instantaneous velocity is the velocity at a point, whereas average velocity is the mean velocity over a certain period of time.
200
What is the limit as x-->0 of ((5cosx)(3^x))
5
200
What is the derivative of f(x)= e^(3x) + 16e^(x)
f'(x)= 3xe^(3x) + 16e^(x)
200
What is the anti-derivative of f'(x)= 9cos(3x)-4
f(x)= 3sin(3x)-4x+C
200
What is the Trapezoidal Rule equal to?
A=(LRAM-RRAM)/2 or A=(1/2)(b1+b2....)h
200
Name the 4 types of Discontinuities
What is Hole, Jump, Infinity, and Oscillating
300
Is 3/(x+3) continuous? If no, at what point is the function discontinuous and what type is it?
No. It is an infinite discontinuity at x=-3
300
What is the line tangent to the curve of
f(x)= 3(x)^(2) - 2x - 5 at x=2
Tangent line of f(x) at x=2 is 10x+3
300
What is f(x) if f''(x)=4 and the velocity at x=2 is 3
f(x)= 2x^(2)-5x+C
300
What is the quotient rule for derivatives?
(lodhi-hidlo)/lo^2
300
A function fails to be differentiable if it has a....
Discontinuity, corner, cusp or a vertical tangent
400
How would you alter this function to make it continuous?
2sin(x+0.5π) x<0
f(x)= 5/2 x=0
(x^2 +4)/(x+2) x>0
Change the 5/2 to 2 at x=0
400
What is the derivative of f(x)= (3x+2) (2x^(2) -4)
f'(x)= 18x^(2) +8x-12
400
What is the integral of (3x^(2))dx if a=0 and b=3
27
400
What does the Mean Value Theorem state?
If y=f(x) is continuous at every point of the closed interval [a,b] and differentiable at every point of its interior (a,b), then there is at least one point c in (a,b) at which
f'(c)=(f(b)-F(a)) / (b-a)
400
What are the intersection points of the following curves
f(x)=x^2-4x-8 and g(x)=-x^2+7x+12.
(-1.44,-0.16) and (6.94,12.41)
500
What is the limit as x-->0+ of 3cosx/(sinx)
Infinity
500
What is the derivative of f(x)= (1+2x^(2)) / x
f'(x)= 2- (1/ x^(2))
500
What is the integral of (sec^(2)x)dx if a=0 and b=π/4
1
500
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫(3t+7)dt at a=-3 and b=x
3x+7
500
Find the area of the region bounded by f(x)=x^2-4x-8 and g(x)=-x^2+7x+12.