Calculus MCQs Question and Answer in Engineering Maths Page-6 section-1

Section 1 Section 2 Section 3

51.
For the function e^-x, the linear approximation around x = 2 is

A. (3 - x)e^-2

B. 1 - x

C. [3 + 2√2 - (1 + √2)x]e^-2

D. e^-2

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52.
The infinite series \[{\text{f}}\left( {\text{x}} \right) = {\text{x}} - \frac{{{{\text{x}}^3}}}{{3!}} + \frac{{{{\text{x}}^5}}}{{5!}} - \frac{{{{\text{x}}^7}}}{{7!}}\,...\,\infty \] converges to

A. cos(x)

B. sin(x)

C. sin h(x)

D. e^x

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53.
If the vector function
\[\overrightarrow {\rm{F}} = {{\rm{\hat a}}_{\rm{x}}}\left( {3{\rm{y}} - {{\rm{k}}_1}{\rm{z}}} \right) + {{\rm{\hat a}}_{\rm{y}}}\left( {{{\rm{k}}_2}{\rm{x}} - 2{\rm{z}}} \right) - {{\rm{\hat a}}_{\rm{z}}}\left( {{{\rm{k}}_3}{\rm{y}} + {\rm{z}}} \right)\]
is irrotational, then the values of the constants k₁, k₂ and k₃ respectively, are

A. 0.3, -2.5, 0.5

B. 0.0, 3.0, 2.0

C. 0.3, 0.33, 0.5

D. 4.0, 3.0, 2.0

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54.
Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x\[ \in \] [-2, 2]?

A. f(x) ≤ 2 |x + 1|

B. f(x) ≤ \[\frac{1}{2}\] |x|

C. f(x) ≤ 2 |x|

D. f(x) ≤ \[\frac{1}{2}\] |x + 1|

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55.
The curve y = x⁴ is

A. concave upward for all values of x

B. concave downward for all x

C. concave up only for positive values of x

D. concave up for negative values of x

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56.
Which one of the following functions is strictly bounded?

A. \[\frac{1}{{{{\rm{x}}^2}}}\]

B. e^x

C. x²

D. e^-x²

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57.
A parametric curve defined by \[{\rm{x}} = \cos \left( {\frac{{\pi {\rm{u}}}}{2}} \right),\,{\rm{y}} = \sin \left( {\frac{{\pi {\rm{u}}}}{2}} \right)\] in the range 0 ≤ u ≤ 1 is rotated about the x-axis by 360°. Area of the surface generated is

A. \[\frac{\pi }{2}\]

B. \[\pi \]

C. \[2\pi \]

D. \[4\pi \]

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58.
Let \[{\rm{g}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{{20}{c}} { - {\rm{x,}}}&{{\rm{x}} \le 1}\\ {{\rm{x}} + 1,}&{{\rm{x}} \ge 1} \end{array}} \right.\] and \[{\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{{20}{c}} {1 - {\rm{x,}}}&{{\rm{x}} \le 0}\\ {{{\rm{x}}^2},}&{{\rm{x}} > 0} \end{array}} \right..\]
Consider the composition of f and g i.e. (fog) (x) = f(g(x)). The number of discontinuities in (fog) (x) present in the interval (\[ - \infty ,\] 0) is:

A. 0

B. 1

C. 2

D. 4

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59.
What is \[\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \theta }}{\theta }\] equal to?

A. θ

B. sin θ

C. 0

D. 1

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60.
A cubic polynomial with real coefficients

A. can possibly have no extrema and no zero crossings

B. may have up to three extrema and upto 2 zero crossings

C. cannot have more than two extrema and more than three zero crossings

D. will always have an equal number of extrema and zero crossings

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Calculus MCQs Question and Answer in Engineering Maths

51. For the function e-x, the linear approximation around x = 2 is

Answer & Solution

52. The infinite series \[{\text{f}}\left( {\text{x}} \right) = {\text{x}} - \frac{{{{\text{x}}^3}}}{{3!}} + \frac{{{{\text{x}}^5}}}{{5!}} - \frac{{{{\text{x}}^7}}}{{7!}}\,...\,\infty \] converges to

Answer & Solution

Answer & Solution

54. Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x\[ \in \] [-2, 2]?

Answer & Solution

55. The curve y = x4 is

Answer & Solution

56. Which one of the following functions is strictly bounded?

Answer & Solution

57. A parametric curve defined by \[{\rm{x}} = \cos \left( {\frac{{\pi {\rm{u}}}}{2}} \right),\,{\rm{y}} = \sin \left( {\frac{{\pi {\rm{u}}}}{2}} \right)\] in the range 0 ≤ u ≤ 1 is rotated about the x-axis by 360°. Area of the surface generated is

Answer & Solution

Answer & Solution

59. What is \[\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \theta }}{\theta }\] equal to?

Answer & Solution

60. A cubic polynomial with real coefficients

Answer & Solution

Read More Section(Calculus)

51.
For the function e^-x, the linear approximation around x = 2 is

52.
The infinite series \[{\text{f}}\left( {\text{x}} \right) = {\text{x}} - \frac{{{{\text{x}}^3}}}{{3!}} + \frac{{{{\text{x}}^5}}}{{5!}} - \frac{{{{\text{x}}^7}}}{{7!}}\,...\,\infty \] converges to

54.
Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x\[ \in \] [-2, 2]?

55.
The curve y = x⁴ is

56.
Which one of the following functions is strictly bounded?

57.
A parametric curve defined by \[{\rm{x}} = \cos \left( {\frac{{\pi {\rm{u}}}}{2}} \right),\,{\rm{y}} = \sin \left( {\frac{{\pi {\rm{u}}}}{2}} \right)\] in the range 0 ≤ u ≤ 1 is rotated about the x-axis by 360°. Area of the surface generated is

59.
What is \[\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \theta }}{\theta }\] equal to?

60.
A cubic polynomial with real coefficients