Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. lim x tends to 0 ex−1−xx2

Question

Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. lim x tends to 0   ex−1−xx2

Melinda Olson · Accepted Answer

Evaluating the numerator and denominator separately yields the indeterminate form 00  limx→0ex−1−xx2=00  Since x2 is nonzero near x=0, and so its derivative 2x, we can use LHospitals rule. Differentiate the numerator and the denominator:  limx→0ex−1−xx2=limx→0d(ex−1−x)dxd(x2)dx  limx→0ex−12x  =00  Use LHospitals rule again:  limx→0ex−12x=limx→0ex2  =e02  =12  Result: limx→0ex−1−xx2=12

Find the limit. Use l’Hospital’s Rule where appropriate. If there

Answered question

Answer & Explanation

New Questions in Calculus 1