| Limits | Derivatives | Theorems | Integrals | Series |
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The value of the function must equal the value of the limit at that point.
In order for a function to be continuous at a point it must….?
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What is 3^x * ln3
What is the derivative of 3^x?
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What is the intermediate value theorem
Which theorem states if a function is continuous on a closed interval and has a derivative on the open interval then the function takes on every value between the interval?
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What is 3x^4/4 + 4x^3+6x^2+c
What is the integral of 3x^3+12x^2+12x?
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What is diverge
Does infinity/n=1 Σ(3/2)^n converge or diverge, if it converges to shut value?
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What is 0
What is the limit as x approaches 1 of the function lnx / x+2?
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What is lo*dhi - hi*dlo all over (lo)^2
What is the basic saying used in the Quotient Rule?
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What is if f is continuous on a closed interval then f has both a maximum value and minimum value on the interval
What is the Extreme value theorem?
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What is -1/3lnlx-2l + 1/3lnlx-5l + c
What is the integral of 1/ (x-2)(x-5)?
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It states a sequence is divergent when the sequence approaches a value other than zero as the sequence’s last term approaches infinity.
What is the nth term test for divergence?
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What is -1/2
What is the limit as x approaches 0 of the function 5x^3+8x^2 / 3x^4-16x^2?
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What is 2cosx*-sinx
What is the derivative of cos^2x
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What is the mean value theorem
What theorem states that if a function is continuous on the closed interval [a,b] and différentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f’(c) is equal to the functions average rate of change over the interval?
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What is 11/2
Solve the differential equation dy/dx = x+2 with the initial condition y(0)=3 and use your solution to find y(1)
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What is k>3
For what values of k will the series infinity/n=1 Σ1/n^2k-5 converge
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When x=0, y=1/0 which is undefined
Explain why y=1/x has a vertical asymptote at x=0?
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What is relative max
If f’ changes sign from positive to negative at a critical point then f has a ….. at that value of x?
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What is the fundamental theorem of calculus
What theorem states that if we can find the anti derivative for the integrand, then we can evaluate the definite integral by evaluating the antiderivative at the endpoints of the interval and subtracting?
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What is 11
If f’(x) = cosx and f(-π) =12, find f(3π/2)
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What is converge conditionally
Does the series infinity/n=1 Σ (-1)^n / n^1/3 converge absolutely, conditionally, or diverge?
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What is L’Hôpital’s rule
What is the rule that provides a technique to evaluate limits of intermediate forms (ex. 0/0) ?
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What is 7/8 per minute
The top of a 25 foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute. When the top of the ladder is 7 feet from the ground, what is the rate of change of the distance between the bottom of the ladder and the wall?
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What is rolle’s theorem
What theorem states that if a function is continuous on the closed interval [a,b] and différentiable on the open interval (a,b) such that f(a)=f(b), then f’(x)=0 for some value within (a,b)?
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What is 125.680
Calculator Active: Find the length of the curve y=x^3 from x=0 to x=5.
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What is 1/57
If the series infinity/n=1 Σ (-1)^n+1 / 5n+2 is approximated by the partial sum with 10 terms, what is the alternating series error bound?
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