Consider the limit expression L= x -2 x-4 as ;x 4

MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Consider the limit expression L=x−2x−4as  x→4.L=\frac{\sqrt{x}-2}{x-4}\quad \text{as}\;x\to 4. Answer the following questions related to LL. (a) Part 1: (i) Show that direct substitution of x=4x=4 in the given expression leads to the indeterminate form 0/00/0. (b) Part 2: (ii) Give a brief explanation, in not more than three sentences, of how a determinate limit can still exist even when direct substitution produces the form 0/00/0. (c) Part 3: (iii) Determine the exact value of LL.

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