Compute the limit
cos(t), et – e-t lim to -, t 2 - 4 > t
Use L'Hospital's rule to find the limit
lim(3 – x?) x->0
find the limits analytically, show all steps
x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....
X+2 X<3 n. lim f(x), where f(x)= { x3 12-2x x>3 3
7. Find the limit. Use L'Hospital's rule if appropriate: > e* + 100x lim x= 3x3 - X
F'(x) < 0 if 0<x< 2or x > 4 f"(x)>0if1<x<3, F"(x)<0if x<lor x>3 4. Find the limit. lim(1-2x) 10 5. What is the minimum vertical distance between the parabolas y = x + 1 and y=x-r 4.pdf
12) Let f(A) = x + 1 xxo 0 x=0 (ax+ 2 x>0 a) Find lim f(x). X-70 b) Find lim F(x). X70 c) Find lim f(x). 13) Let f(x) = x - x .O 12.1 x 0 a) Find lim f(x). 6) Find
8. For the function graphed in the accompanying figure, find (a) lim (x) (b) lim 0(x) (c) lim (x) (d) (4). y = 0(2) Figure Ex-8
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
(Hint: think of tan as a fraction!) lim (1 - .) tan 7. Suppose a function f(x) satisfies f'(x) < 0 and f(x) > 0 for all x 20. > 0 for all x > 0. Consider the function F(x) := ["s(t) dt whose domain is 0,00). Is F(x) an increasing or decreasing function