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Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives1 Mark
Question
Write the value of $\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{xf}(\text{a})-\text{af}(\text{x})}{\text{x}-\text{a}}$
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Answer

$\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{xf}(\text{a})-\text{af}(\text{x})}{\text{x}-\text{a}}=\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{xf}(a)-\text{af}(\text{x})+\text{af}(\text{a})-\text{af}(\text{a})}{\text{x}-\text{a}}$$\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{f}(\text{a})(\text{x}-\text{a})-\text{a}(\text{f}(\text{x})-\text{f}(\text{a}))}{\text{x}-\text{a}}$
$=\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{f}(\text{a})(\text{x}-\text{a})}{(\text{x}-\text{a})}-\text{a}\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{f}(\text{x})-\text{f}(\text{a})}{\text{x}-\text{a}}$
$=\text{f}(\text{a})-\text{a}\text{f}'(\text{a})$

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