we will use two rules of limit
#1
L'Hospital rule
If
OR 
where a can be any real number, infinity or negative infinity. then
where f’(x) and g’(x) are
differentiation of f(x) and g(x) respectively
#2
leibiniz rule of differentiating definite integral
![[sh g(t)dt] = = g(h())(c) - 9(f(:))f(:1)](http://img.homeworklib.com/questions/adae5550-38bf-11eb-9c25-3fcbf7379c55.png?x-oss-process=image/resize,w_560)
h' and f' are differentiation of h and f respectively

3. Evaluate the limits x-2 (a) lim 2 (c) lim x-,2x2 +2 ?- (b) lim 2 im 2x +4 (d) Given f(x)x1 -1<x s 2 3-?
4. Evaluate the limit (4pts each) 9x4+x (a) lim x -3 (b) lim Vx +25
4. Evaluate the limit (4pts each) 9x4+x (a) lim x -3 (b) lim Vx +25
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cewise Functions e function, evaluate lim f(x). 2 1-2x²+x+3 f(x) = { 2x2 – 3x + 3 (-3x - 2 if if xs1 1<x< 6 if x26 below:
1. Evaluate lim f(x) if 1 – x4 = f(x) < cosx for all x in X+0 2. Find f'(x) when (a) f(x) = cscZx - cotax (b) f(x) = Vă -
3) Use L'Hopital's Rule to evaluate and check your answers numerically: - sin x (a) lim x+0+ х 1 (b) lim X-70
1. (25 points) Evaluate the limit, if it exists. lim (x3 + 3x² 3 1+ 4x2 + 3.14) 2+1 (b) lim 29- - 9 x² - x - 20 (c) lim 1- -5 5