Limit of a Function

Problems based on special limits and Limit of the functions having Limit inbuilt

The left hand limit of the function f(x)=4

Find the sum of an infinite geometric series whose first term is the limit of the function f( x) =( tan x - sinx )/( sin^(3) x ) as x rarr 0 and whose common ratio is the limit of the function g(x) = ( 1-sqrt(x))/( (cos^(-1)x ) as x rarr 1

Find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(tan x-sin x)/(sin^(3)x) as x rarr0 and whose common ratio is the limit of the function g(x)=(1-sqrt(x))/((cos^(-1)x)^(2)) as x->1

Evaluate right-handed limit of the function : f(x)={{:(abs(x-3)/(x-3)",",x ne 3), (" 0,", x=3):} at x = 3.

Evaluate left-handed limit of the function : f(x)={{:(abs(x-3)/(x-3)",",x ne 3), (" 0,", x=3):} at x = 3.

Find the sum of an infinite geometric series whose first term is the limit of the function f(x)=(1-tan x)/(1-sqrt(2)sin x) as x rarr(pi)/(4) and whose common ratio is the limit of the function g(x)=(1-sqrt(x))/((cos^(-1)x)^(2)) as x rarr1

Show that left and right limits of function f(x)=(log_(e)x)/(x-1) at x=1 are equal and their value is 1

Consider the function f(x) = 2x + 3 and we want to find the limit of this function at x = 1.

Evaluate the left-and right-hand limits of the function f(x)={(|x-4|)/(x-4),x!=4 0,x=4a tx=4