Define h(x)= cases x^2-9 x-3 , & x3

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Define

h(x)=\begin{cases} \dfrac{x^2-9}{x-3}, & x<3,\\ k, & x=3,\\ \dfrac{2x+m}{x-3}, & x>3. \end{cases}

Here

k

and

m

are real parameters. (i) Find the value of the common one–sided limit of

h(x)

x\to3

that is required for continuity. (ii) Obtain the condition connecting

k

and

m

so that

h

is continuous at

x=3

. (iii) Determine the range of values of

m

for which such a real number

k

exists, and for each permissible

m

give the corresponding

k