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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
Question
Fill in the blanks.
If $\text{y}=1+\frac{\text{x}}{1!}+\frac{\text{x}^{2}}{2!}+\frac{\text{x}^{3}}{3!}+....$ then ____________.
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Answer

If $\text{y}=1+\frac{\text{x}}{1!}+\frac{\text{x}^{2}}{2!}+\frac{\text{x}^{3}}{3!}+....$then $\frac{\text{dy}}{\text{dx}}=\text{y}.$Solution:
Given that $\text{y}=1+\frac{\text{x}}{1!}+\frac{\text{x}^{2}}{2!}+\frac{\text{x}^{3}}{3!}+....$ $\frac{\text{dy}}{\text{dx}}=0+\frac{1}{1!}+\frac{2 \text{x}}{2!}+\frac{3\text{x}^{2}}{3!}+......$ $=1+\frac{\text{x}}{1!}+\frac{\text{x}^{2}}{2!}+\frac{\text{x}^{3}}{3!}+....=\text{y}$ Hence, the value of the filler is y.

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