Find the value of 'a' and 'b' `lim_(x to 2) and lim_(x to 4)` exists where
`f(x){{:(x^(2)+ax+b,0lexlt2),(3x+2,2lexle4),(2ax+5b,4ltxle8):}`

Find the values of a and b so that the function f(x) defined by f(x)={(x^2 +ax+b),(0<=x<2),(3x+2) , (2<=x<=4), (2a x+5b), (4 < x <= 8)} becomes continuous on [0,pi].

Calculate lim_(x to 2) , where f(x) = {{:(3 if ,x le 2),(4 if, x gt 2):}

Evaluate, lim_(x to 2) (x^(3) - 8)/(x^(2) - 4)

Find the values of a and b, if x^2-4 is a factor of ax^4+2x^3-3x^2+bx-4.

Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):} and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxlt3),(x^(2)+b+1,,3gexle4):} lim_(xrarr2) (f(x))/(|g(x)|+1) exists and f is differentiable at x = 1. The value of limit will be

Evaluate lim_(x to 2) [(x^(2) - 4)/(2x + 2)]

Evaluate lim_(x to 2) [4x^(2) + 3x + 9]

It is given that f(x) = (ax+b)/(x+1) , Lim _(x to 0) f(x) and Lim_(x to oo) f(x) = 1 Prove that fx(-2) = 0 .

lim_(x to -1) (x^(8)+x^(4)-2)/(x-5)

Evaluate lim_(x to 0) [(3x^(2) + 4x + 5)/(x^(2) - 2x + 3)]