Question

If ƒ(1) = g(1) = 2 and ƒ′(1), g′(1) exist then evaluate

(\frac{ƒ(1)g(x) - ƒ(1) - g(1)ƒ(x) + g(1)}{g(x) - ƒ(x)})

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (B)

2

Answer 2

Here, the form is .

∴ limit = $\lim _ { x \rightarrow 1 }$  

{using L’ Hospital’s rule}

=  $\lim _ { x \rightarrow 1 }$ $\frac { 2 \left\{ \mathrm {~g} ^ { \prime } ( \mathrm { x } ) - f ^ { \prime } ( \mathrm { x } ) \right\} } { \mathrm { g } ^ { \prime } ( \mathrm { x } ) - f ^ { \prime } ( \mathrm { x } ) }$ = $\lim _ { x \rightarrow 1 }$ 2 = 2.