11th Maths Monthly Test - 4 ( Differential Calculus - Limits and Continuity )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Differential Calculus - Limits and Continuity ) -Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

Discuss continuity of (x) =\(\sqrt{1-x^2}\)wher x u0aa6 [-1,1]

Evaluate the following limits :\(\underset{x\rightarrow 0}{lim}{e^{ax}-e^{bx}\over x}\)

Evaluate the following limits : \(\underset{x\rightarrow2}{lim}{2-\sqrt{x+2}\over {\sqrt[3]{2}}-{\sqrt[3]{4-x}}}\)

Sketch the graph of a function f that satisfies the given values :
f(- 2) = 0
f(2) = 0
\(\underset{x\rightarrow -2}{lim}f(x)=0\)
\(\underset{x\rightarrow -2}{lim}f(x)\) does not exist.

Find the constant b that makes g continuous on \((-\infty,\infty)\) g(x) = \(\begin{cases} { x }^{ 2 }-{ b }^{ 2 } & if\ x<4 \\ bx+20 & if\ x\ge 4 \end{cases}\)

Evaluate \(\lim _{ x\rightarrow \frac { 1 }{ \sqrt { 2 } } }{ \frac { x-\cos { (\sin ^{ -1 }{ (x) } ) } }{ 1-\tan { (\sin ^{ -1 }{ x } ) } } } \)

Evaluate the following limits :\(\underset{x\rightarrow0}{lim}{\sqrt{1+x^2}-1\over x}\)

If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?

According to Einstein’s theory of relativity, the mass m of a body moving with velocity v is m =\({m_O\over \sqrt{1-{v^2\over c^2}}},\) where m₀ is the initial mass and c is the speed of light. What happens to m as \(v\rightarrow{c}^-\) Why is a left hand limit necessary?

Evaluate the following limits :\(\underset{x\rightarrow0}{lim}{e^x-e^{-x}\over sin x}\)

Which of the following functions f has a removable discontinuity at x = x₀? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R
\(f(x)={x^3+64\over x+4},x_o=-4\)

Evaluate : \(lim_{x \rightarrow {\pi\over 4}}{4\sqrt{2}-(cos \ x+sin \ x)^5\over 1-sin 2x}\)

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11th Maths Monthly Test - 4 ( Differential Calculus - Limits and Continuity )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Differential Calculus - Limits and Continuity ) -Aug 2020

Part - A

Generic 5 - Answer All Question

Discuss continuity of (x) =\(\sqrt{1-x^2}\)wher x u0aa6 [-1,1]

Evaluate the following limits :\(\underset{x\rightarrow 0}{lim}{e^{ax}-e^{bx}\over x}\)

Evaluate the following limits : \(\underset{x\rightarrow2}{lim}{2-\sqrt{x+2}\over {\sqrt[3]{2}}-{\sqrt[3]{4-x}}}\)

Sketch the graph of a function f that satisfies the given values : f(- 2) = 0 f(2) = 0 \(\underset{x\rightarrow -2}{lim}f(x)=0\) \(\underset{x\rightarrow -2}{lim}f(x)\) does not exist.

Find the constant b that makes g continuous on \((-\infty,\infty)\) g(x) = \(\begin{cases} { x }^{ 2 }-{ b }^{ 2 } & if\ x<4 \\ bx+20 & if\ x\ge 4 \end{cases}\)

Evaluate \(\lim _{ x\rightarrow \frac { 1 }{ \sqrt { 2 } } }{ \frac { x-\cos { (\sin ^{ -1 }{ (x) } ) } }{ 1-\tan { (\sin ^{ -1 }{ x } ) } } } \)

Evaluate the following limits :\(\underset{x\rightarrow0}{lim}{\sqrt{1+x^2}-1\over x}\)

If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?

According to Einstein’s theory of relativity, the mass m of a body moving with velocity v is m =\({m_O\over \sqrt{1-{v^2\over c^2}}},\) where m0 is the initial mass and c is the speed of light. What happens to m as \(v\rightarrow{c}^-\) Why is a left hand limit necessary?

Evaluate the following limits :\(\underset{x\rightarrow0}{lim}{e^x-e^{-x}\over sin x}\)

Which of the following functions f has a removable discontinuity at x = x0? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R \(f(x)={x^3+64\over x+4},x_o=-4\)

Evaluate : \(lim_{x \rightarrow {\pi\over 4}}{4\sqrt{2}-(cos \ x+sin \ x)^5\over 1-sin 2x}\)

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Sketch the graph of a function f that satisfies the given values :
f(- 2) = 0
f(2) = 0
\(\underset{x\rightarrow -2}{lim}f(x)=0\)
\(\underset{x\rightarrow -2}{lim}f(x)\) does not exist.

According to Einstein’s theory of relativity, the mass m of a body moving with velocity v is m =\({m_O\over \sqrt{1-{v^2\over c^2}}},\) where m₀ is the initial mass and c is the speed of light. What happens to m as \(v\rightarrow{c}^-\) Why is a left hand limit necessary?

Which of the following functions f has a removable discontinuity at x = x₀? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R
\(f(x)={x^3+64\over x+4},x_o=-4\)