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AP Calculus Midterm
| Question | Answer |
|---|---|
| When Finding An Anti-Derivative, Always Add The Variable... | c |
| Left-Hand Riemann Sum Estimate | over-approximation |
| Right-Hand Riemann Sum Estimate | under-approximation |
| Mid-Point Riemann Sum Estimate | average-approximation |
| If Number On Top Of The Integrate Symbol Is Greater Than The One Below... | switch their places and insert a negative |
| In Integrals, The Constants Can Be... | taken out and placed in front of the symbol |
| In An Integral, You Can Separate... | any addition and subtraction within it and integrate separately |
| When Finding dy/dx... | add a y' every time you derive a y |
| Solve An Equation On A Calculator | solve(y1,x) |
| To Evaluate At Sign On Calculator | | |
| Evaluate A Derivative At A Certain Value On Calculator | d(y1(x),x) | x=1 |
| EVT | if f(x) is continuous at [a,b], then f(x) is guaranteed to have an absolute maximum and minimum on [a,b] |
| When Using EVT, Check... | all critical values & endpoints |
| Average Rate Of Change | slope of secant = y2-y1/x2-x1 |
| Instantaneous Rate Of Change | slope of tangent line = f'(x) |
| MVT | if f(x) is continuous on [a,b] and differentiable on (a,b), then it is guaranteed to exist a value of c where f'(c)=f(b)-f(a)/b-a |
| IVT | if f(x) is continuous on [a,b] and f(a) ≤ k ≤ f(b), there exists at least one value, x=c, on (a,b) such that f(c)=k |
| Derivative Of tan(x) | sec^2(x) |
| Derivative Of csc(x) | -cot(x)csc(x) |
| Derivative Of sec(x) | tan(x)sec(x) |
| Derivative Of cot(x) | -csc^2(x) |
| Derivative Of e^any | (e^any) x (d/dx any) |
| Derivative Of ln(any) | (1/any) x (d/dx any) |
| Derivative Of a^any | (a^any) x (ln a) x (d/dx any) |
| Derivative Of loga(any) | (1/any) x (1/lna) x (d/dx any) |
| Value Of ln(1) | 0 |
Created by:
abievans
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