Let `f (x) =(ax+b)/(x+1), lim_(x rarr 0)f(x)=2` and `lim_(x to oo)f(x)=1 `, Prove that f (- 2) = 0.

lim_(x rarr 0) (|x|)/x is :

Find lim_(x to 2)f(x) , where f(x) = 3|x| - 2

Find lim_(x to 0)f(x) , when f(x) = (5x + 2) .

Find lim_(x rarr 0) f(x) , where f (x) =|x|-5.

lim_(x rarr 0) ((x+1)^5-1)/x is :

Find lim_(x rarr 0)f(x) and lim_(x rarr 1) f(x) , where f(x)={(2x+3,xle0),(3(x+1),x>0):}

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is a. ((12)/(25),(-9)/(25)) b. ((12)/(25),(9)/(25)) c. ((16)/(25),(-8)/(25)) d. ((24)/(25),(-7)/(25))

Find lim_(x rarr 0) f(x) , and lim_(x rarr 1) f(x) , where : f(x)= {(2x+3,",",xle0),(3(x+1),",", x>0.):}

Consider the function f (x) = 1/x^2 for x > 0. To find lim_(x to 0) f(x) .

Consider the function : f (x) ={(x-2,x 0):} . To find lim_(x to 0) f(x) .