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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Show that f(x) = x2 is continuous and differentiable at x = 0

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प्रश्न

Show that f(x) = x2 is continuous and differentiable at x = 0

बेरीज
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उत्तर

R f'(0) = `lim_("h" -> 0^+) ("f"(0 + "h") - "f"(0))/"h"`

= `lim_("h" -> 0) ("h"^2 - 0)/"h"`     ...[∵ f(x) = x2]

= `lim_("h" -> 0) "h"`   ...[∵ h → 0 ∴ h ≠ 0]

= 0

Similarly, it can be shown that L f'(0) = 0

∴ R f'(0) = L f'(0) = 0

∴ f is differentiable at x = 0

and hence continuous at x = 0.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differentiation - Exercise 9.1 [पृष्ठ १८८]

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