Use analytical methods to evaluate lim (Vx-8-Vx-6) What is the most efficient wa

Question

Use analytical methods to evaluate lim (Vx-8-Vx-6) What is the most efficient way for this limit to be evaluated? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The limit can be evaluated by direct substitution. OB. Manipulate the given expression algebraically to rewrite the limit as im ° C. Use l'H pital's Rule directly to rewrite the limit as lim O D. (Simplify your answer.) Use the substitution tand then l'Hôpital's Rule to rewrite the limit as lim t+0

Explanation / Answer

We have given lim x-->infinity (sqrt(x-8)-sqrt(x-6))

multiply by the conjugate of sqrt(x-8)-sqrt(x-6)

lim x-->infinity (sqrt(x-8)-sqrt(x-6))=lim x-->infinity (sqrt(x-8)-sqrt(x-6))*(sqrt(x-8)+sqrt(x-6))/(sqrt(x-8)+sqrt(x-6))

=lim x-->infinity (x-8-x+6)/(sqrt(x-8)+sqrt(x-6))

=lim x-->infinity (-2)/(sqrt(x-8)+sqrt(x-6))

=-2*lim x-->infinity (1/(sqrt(x-8)+sqrt(x-6)))

=-2*(1/(infinity+infinity)) since sqrt(x-8)=infinity,sqrt(x-6)=infinity

=-2*(1/infinity)

=-2*0 since 1/infinity =0

=0

lim x-->infinity (sqrt(x-8)-sqrt(x-6))=0

answer is B. Manipulate the given expression algebraically to rewrite the limit as

lim x-->infinity (-2)/(sqrt(x-8)+sqrt(x-6))=0

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.