(a) If {\f}(x)={\\begin{array}{ccc}x^2 & & \\\\text{ if }\\ x \geq 1 \ x & & \\\\text{ if }\\ x&lt\ 1\end{array}., then show that {\f} is not differentiable at x=1. OR (b) Find the value(s) of ' \lambda ', if the function f(x)={\\begin{array}{c}\\\{ \sin \\\^2 \lambda x\end\frac{array}{x^2}, , \text{ if } x \neq 0 \text{ is continuous at } x=0 . ; 1, , \text{ if } x=0 }.

CBSE Class 12 Math 2023 Delhi Set 1 Solved Paper - Question 22

Question : 22 of 38

Marks: +1, -0

(a) If

{\f}(x)={\{\table x^2, , \;\text " if "\; x ≥ 1 ; x, , \;\text " if "\; x< 1}.

, then show that

{\f}

is not differentiable at

x=1

.
OR
(b) Find the value(s) of '

λ

', if the function

f(x)={\{\table \;{ sin \;^2 λ x}/{x^2}, , \;\text " if "\; x ≠ 0 \;\text " is continuous at "\; x=0 . ; 1, , \;\text " if "\; x=0 }.

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