(a) Find the value of {\k} for which the function {\f} given as f(x)={\\begin{array}{c}\\\{1-\cos x\end\frac{array}{2 x^2}, \text{ if } x \neq 0 ; {\k} ,{, } \text{ if } x=0}. is continuous at x=0. OR (b) If x= {\a} \cos {\t} and {\y}= {\b} \sin {\t}, then find { {\d}^2 {\y}}/{ {\d} x^2}.

CBSE Class 12 Math 2023 Delhi Set 3 Solved Paper - Question 7

SECTION - B

This section comprises of Very Short Answer (VSA) type questions of 2 marks each.

Question : 7 of 12

Marks: +1, -0

(a) Find the value of

{\k}

for which the function

{\f}

given as

f(x)={\{\table \;{1-\cos x}/{2 x^2}, \;\text " if "\; x ≠ 0 ; {\k} ,{, \;} \;\text " if "\; x=0}.

is continuous at

x=0

.
OR
(b) If

x= {\a} \cos {\t}

and

{\y}= {\b} sin \; {\t}

, then find

\;{ {\d}^2 {\y}}/{ {\d} x^2}

Solution:

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