CBSE 12th Standard Maths Subject Continuity and Differentiability HOT Questions Fill Ups Questions With Solution 2021
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CBSE 12th Standard Maths Subject Continuity and Differentiability HOT Questions Fill Ups Questions With Solution 2021
12th Standard CBSE
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Reg.No. :
Maths
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Write the derivative of the function f(x) = tan-1 \(\sqrt { sinx } \) w.r.to x
(a)\(\left\{ \frac { cosx }{ 2\sqrt { sinx } \left( 1+sinx \right) } \right\} \)
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Is it true that log (xsinx+cossinx x)=sinxlogx+sin x logcos x?
(a){No}
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Discuss the continuity of the cosine, cosecant, secant and cotangent functions.
(a){Not applicable}
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Discusss the continuity of the function f(x) = sin|x|
(a){continous}
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CBSE 12th Standard Maths Subject Continuity and Differentiability HOT Questions Fill Ups Questions With Solution 2021 Answer Keys
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\(\left\{ \frac { cosx }{ 2\sqrt { sinx } \left( 1+sinx \right) } \right\} \)
\(\left\{ \frac { cosx }{ 2\sqrt { sinx } \left( 1+sinx \right) } \right\} \)
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If x = f(t) and y = g(t), then is \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } =\frac { { d }^{ 2 }y/{ dt }^{ 2 } }{ { d }^{ 2 }x/{ dt }^{ 2 } } \) ?
{No}If x = f(t) and y = g(t), then is \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } =\frac { { d }^{ 2 }y/{ dt }^{ 2 } }{ { d }^{ 2 }x/{ dt }^{ 2 } } \) ?
{No} -
\(=\lim _{h \rightarrow 0} f(x)=\lim _{h \rightarrow 0} \cos x=\cos a[\therefore f(x)=\cos x]\)
f(a) = cos a
\(\therefore \lim _{x \rightarrow a} f(x)=f(a)\)
Thus, f(x) is continuous at x=a. But a is an arbitrary points so f(x) is continuous at all points.
So, f(x) is continuous at all points.
(ii) Here, f(x) = cosec x. Since, f(x) is not defined at × = nπ, nϵZ.Thus, f(x) is continuous at all points except x = nπ, n ϵ Z(iii) Here, f(x)sec x
Since, f(x) is not defined at \(x=(2 n+1) \frac{\pi}{2^{\prime}}, n \in Z .\)
Thus, f(x) is continuous at all points except \(x=(2 n+1) \frac{\pi}{2}, n \in Z\)
(iv) Here, f(x) = cotx
SInce, f(x) is not defined at x = n π, nϵZ.
Thus, f(x) is continuous at all points excepts x = nπ, nϵZ\(=\lim _{h \rightarrow 0} f(x)=\lim _{h \rightarrow 0} \cos x=\cos a[\therefore f(x)=\cos x]\)
f(a) = cos a
\(\therefore \lim _{x \rightarrow a} f(x)=f(a)\)
Thus, f(x) is continuous at x=a. But a is an arbitrary points so f(x) is continuous at all points.
So, f(x) is continuous at all points.
(ii) Here, f(x) = cosec x. Since, f(x) is not defined at × = nπ, nϵZ.Thus, f(x) is continuous at all points except x = nπ, n ϵ Z(iii) Here, f(x)sec x
Since, f(x) is not defined at \(x=(2 n+1) \frac{\pi}{2^{\prime}}, n \in Z .\)
Thus, f(x) is continuous at all points except \(x=(2 n+1) \frac{\pi}{2}, n \in Z\)
(iv) Here, f(x) = cotx
SInce, f(x) is not defined at x = n π, nϵZ.
Thus, f(x) is continuous at all points excepts x = nπ, nϵZ -
{continous}
{continous}
