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Expert: Sherry Wallin - 10/15/2009


Question

calculus limit questio
Hi Sherry, I'm having trouble solving this problem (see attach image). I know you can't use the direct substitution but you'll end up with a zero on the denominator and that's against the rule. So I would have to rationalize the expression right? But I keep getting zero as my answer...

Answer
Hi Sue~]
    Use L'Hospital's Rule for indeterminate forms: if lim(x->a) [f(x)/g(x)] = 0/0 this is an indeterminate form and if f and g are differentiable and g'(x) != 0 near a, except possibly at a, then the limit of the quotient is equal to the lim of the quotient of their derivatives. Here let b be our variable so you have lim(b->25)[f(b)/g(b)]=0/0 and both 25-b and 5-sqrtb are differentiable and the derivative of 5-sqrtb is nonzero near 25 except at 25 so lim(b->25)[f'(b)/g'(b)]=
lim(b->25)[-1/(-1/2)b^(-1/2)] = lim(b->25)2sqrtb = 2*5 = 10.

Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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