Homework SourseCompute the following limits SHOW WORK PLEASE a limit as x
Compute the following limits: SHOW WORK PLEASE !
a) limit as x approaches 2 of sin(ax) where a is a constant
b) limit as x approaches 0 of (1-cos(x))/x^2
c) limit as x approaches -infinity of (e^x)/(x^3)
d) limit as x approaches 0+ of x^x
e) limit as x approaches infinity of (sqrt(x^2+x-1)-x)
a) limit as x approaches 2 of sin(ax) where a is a constant
b) limit as x approaches 0 of (1-cos(x))/x^2
c) limit as x approaches -infinity of (e^x)/(x^3)
d) limit as x approaches 0+ of x^x
e) limit as x approaches infinity of (sqrt(x^2+x-1)-x)
Solution
a) sin 2a b) 1 - cosx / x*X = 2 sinx/2 sinx/2 / x*x = 1/2 c) put x -> infintiy : -1/e^x *(x^3) = 0 d) take logy = x lnx : 0 : y = 1 e) sqrt[x*x + x - 1] - x : x - 1 / sqrt[x*x + x - 1] + x : 1/2 answer !!!
