| Hints | Answers |
|---|
| Continuous (condition one): if f(a) | |
| Continuous if: f(a) __ lim (as x-->a) f(x) | |
| Finding the derivative is the same as finding the ___________ line | |
| If f '' (x) > 0 for every x in (a , b), then f is | |
| Evaluate: lim (as x-->0) (sin(x))/x | |
| If f is continuous on [a , b] and differentiable on (a , b), then there is at least one number c in (a , b) such that (f(b)-f(a)) / (b-a)=f ' (c) | |
| Evaluate: lim (as x-->0) (1-cos(x))/x | |
| If f is continuous on [a, b], f(a) does not equal f(b), and k is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c)=k | |
| If f(x) approaches infinity (+ or - ) as x approaches c from the right of left, then the line x=c is a __________ __________ of the graph of f. | |
| Evaluate: lim (x--> infinity) (6x^3-8x+2)/(5x^3+9) | |
| Evaluate: lim (x--> infinity) (7x^4)/(3^3) | |
| Evaluate: lim (x--> infinity) (x^5/x^6) | |
| If f ' (x) > 0 for every x in (a , b), then f is | |
| If f '' (x) < 0 for every x in (a , b), then f is | |
| If f ' (x) < 0 for every x in (a , b), then f is | |
| If f is continuous on [a , b] and differentiable on (a , b) such that f(a) = f(b), then there is al teast one number c in the open intercal (a, b) such the f '(c)=0 | |
| | Hints | Answers |
|---|
| Evaluate: lim (as x-->0) cos(x) | |
| If lim f(x) approaches two different numbers from the right and left sides then the limit | |
| Must consider the ___________ in locating the maximum and minimum values of a function | |
| If f is differentiable at x=c, then f is __________ at x=c | |
| Name the rule: (d/dx) [ f(x) + g(x) ] = f ' (x) + g ' (x) | |
| Derivative of velocity | |
| Name the rule: (d/dx) [ f(x)g(x) ] = f ' (x) g(x) + f(x) g'(x) | |
| derivative of csc (x) = | |
| The ______ Rule derivative [f(g(x))]= f ' (g(x)) g ' (x) | |
| lim as x approaches infinity of (8x^4+5x^2+3x^5)/(x^4+4) = 3x = | |
| Find the slope of the graph: f(x)= 3x^7+2x^4-5x+6 --> f'(x)= | |
| Whats the acceleration when the s(t)= t^4+6t^2+3t --> a(c)= | |
| Whats the Average Rate of Change for f(x)=t^2+2t over interval [-1,3] | |
| Differentiate the function: h(x)= -4/(8x^2) --> h'(x)= | |
| Find critical numbers for f'(x)= x^2-2x-15 | |
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