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x = 0 पर, f(x) = `{{:(x^2 sin 1/x",", "यदि" x ≠ 0),(0",", "यदि" x = 0):}`
Concept: undefined >> undefined
x = 2 पर, f(x) = `{{:(1 + x",", "यदि" x ≤ 2),(5 - x",", "यदि" x > 2):}`
Concept: undefined >> undefined
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दर्शाइए कि x = 5 पर, f(x) = |x – 5| संतत है, परंतु अवकलनीय नहीं है।
Concept: undefined >> undefined
एक फलन f: R → R सभी x, y ∈R, f (x) ≠ 0 के लिए समीकरण f (x +y)=f (x) f (y) को संतुष्ट करता है। मान लीजिए कि यह फलन x = 0 पर अवकलनीय है तथा f ′ (0) = 2 है। सिद्ध कीजिए कि f ′(x) = 2 f (x) है।
Concept: undefined >> undefined
`log (x + sqrt(x^2 + "a"))`
Concept: undefined >> undefined
`sin sqrt(x) + cos^2 sqrt(x)`
Concept: undefined >> undefined
`cos(tan sqrt(x + 1))`
Concept: undefined >> undefined
sinx2 + sin2x + sin2(x2)
Concept: undefined >> undefined
`sin^-1 1/sqrt(x + 1)`
Concept: undefined >> undefined
(x + 1)2(x + 2)3(x + 3)4
Concept: undefined >> undefined
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
Concept: undefined >> undefined
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
Concept: undefined >> undefined
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
Concept: undefined >> undefined
`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` तथा `"a"/"b" tan x > -1`
Concept: undefined >> undefined
