Question 6: Show that, if a > 0, then lim (I.) = 0. (Hint: Mimic Example...
Vx+1-1 Evaluate: lim x>0 х Please solve it in detail and show all your steps./
6. Let si = 4 and sn +1 (sn +-) for n > 0. Prove lim n→oo sn exists and find limn-oo Sn. (Hint: First use induction to show sn 2 2 and the.show (sn) is decreasing)
wa I LOSERS DETAILS SCALCET8 2.5.039. 0/2 Submissions Used MYN Show that is continuous on (-0, co). S1 - x? ifx51 if x > 1 On the interval (--0,1), fis ---Select- function; therefore fis continuous on (-0, 1). On the interval (1, .), fis-Select- function; therefore ris continuous on (1,co). At x = 1, limf(x) - lim and lim MX) - lim 1)-1 solim P(x) Also, (1) - Thus, ris continuous at x = 1. We conclude that is continuous...
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....
QUESTION 3 Find the limit. lim (x,y)-> (1, 2) * In y O In (2) - 1 In 2 o 2 No limit
4. Show that lim -oxsin(1/2) = 0 by by appealing directly to the definition of limit. Recall that -1 < sin < 1. 5. Define a function that is nowhere continuous and another function that is continuous only at one point in its domain.
(5) (Bonus question): Give and example of functions y () and y () such that lin/(z) = 0 but lim o zl = 8. The important point of such an example is that even if the numerator of a quotient has a limit of 0, you are not justified in concluding the limit of the quotient is O
(5) (Bonus question): Give and example of functions y () and y () such that lin/(z) = 0 but lim o zl...
part (c)
7.23. Let y(x) = n²x e-nx. (a) Show that lim, - fn(x)=0 for all x > 0. (Hint: Treat x = 0 as for x > 0 you can use L'Hospital's rule (Theorem A.11) - but remember that n is the variable, not x.) (b) Find lim - So fn(x)dx. (Hint: The answer is not 0.) (c) Why doesn't your answer to part (b) violate Proposition 7.27 Proposition 7.27. Suppose f. : G C is continuous, for n...
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
(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