14. Use L'Hospital's rule to prove that a" = win"), for every real a > 1...
Use L'Hospital's rule to find the limit
lim(3 – x?) x->0
Suppose a is a real number and 1 + a > 0. Prove that (1 + a)" > 1+ na for every integer n > 1.
7. Find the limit. Use L'Hospital's rule if appropriate: > e* + 100x lim x= 3x3 - X
Prove that for every positive real (important: is not
necessarily an integer), that
.
Hint: For every , the function
is
strictly growing.
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use all 3 cases please
0. Prove that for every real number x, if -3| > 3 then x2 > 6x. Proof: Given |x - 3]> 3.
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. 1 lim X + In x x+1 1+ cos 50X
Use series to evaluate the limit. Solutions using l'Hospital's rule will not be given credit. : - In(1+0) (a) lim 2012 1- COSI (b) lim >01+- et
x 30 4.(5 pts) Find the limit. Use l'Hospital's Rule if appropriate. limx40 32-1
Question 13 0.14 pts Use L'Hospital's rule to evaluate In(x + 1) – lim 1 cos(3x) 20 1 9 1 0 On 1 3 O -1 0
Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim, 0 2x+cos 2-3 sino 1+36x3-1 (b) lim;-+0 sin(60)(et-1-2)