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)) / (ba)=f ' (c)  
Evaluate: lim (as x>0) (1cos(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^38x+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^45x+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^22x15  
