10 Can someone please help me with this limit thanks for you

10.

Can someone please help me with this limit? thanks for your help!

Find the limit of f(x) = 6x4+7x3+2/4x5 as x approaches » and as x approaches - infinity

Solution

When x approaches to infinity if we will apply the limiting value that will give the undetermined form infinity/infinity so, we need to simplify the limit function first. limit x approaches to infinity ((6x^4 + 7x^3 + 2)/4x^5) we can rewrite it as limit x approaches to infinity( 6x^4/4x^5 + 7x^3/4x^5 + 2/4x^5) or, limit x approaches to infinity( 6x^4/4x^5) + limit x approaches to infinity( 7x^3/4x^5) + limit x approaches to infinity( 2/4x^5) limit x approaches to infinity(3/2x) + limit x approaches to infinity 7/4x^2 + limit x approaches to infinity1/2(x^(5) ===> applying the limiting value will result 3/infinity + 7/infinity + 1/infinity = 0 as we know that 1/infinity = 0 we will get the same result for negative infinity hope this will help you!