Let . Answer the following…

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

Problem

Let

f(x)=\dfrac{x^{3}-3x+2}{x+1}

. Answer the following questions. (i) Explain why the limit

\displaystyle \lim_{x \to 2} f(x)

can be obtained directly by substituting

x=2

in the expression for

f(x)

. (ii) Calculate

\displaystyle \lim_{x \to 2} f(x)

, showing each step of your working. (iii) Substituting

x=-1

f(x)

leads to the form

0/0

. Explain why direct substitution fails at

x=-1

and state one algebraic step that would be required before evaluating the limit at that point (do not perform the full calculation).