Students can download 11th Business Maths Chapter 5 Differential Calculus Ex 5.10 Questions and Answers, Notes, Samcheer Kalvi 11th Business Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 11th Business Maths Solutions Chapter 5 Differential Calculus Ex 5.10

Samacheer Kalvi 11th Business Maths Differential Calculus Ex 5.10 Text Book Back Questions and Answers

Question 1.
If f(x) = x2 – x + 1 then f(x + 1) is:
(a) x2
(b) x
(c) 1
(d) x2 + x + 1
Answer:
(d) x2 + x + 1
Hint:
f(x) = x2 – x + 1
f(x + 1) = (x + 1)2 – (x + 1) + 1
= x2 + 2x + 1 – x – 1 + 1
= x2 + x + 1

Question 2.
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q2
(a) -1
(b) 2
(c) 5
(d) 7
Answer:
(c) 5
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q2.1
f(5) = 52 – 4(5) = 25 – 20 = 5
[For x = 5 take f(x) = x2 – 4x]

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 3.
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q3
(a) 2
(b) 5
(c) -1
(d) 0
Answer:
(a) 2
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q3.1
f(0) = 0 + 2 = 2
[For x = 0 take f(x) = x + 2]

Question 4.
If f(x) = \(\frac{1-x}{1+x}\) then f(-x) is equal to:
(a) -f(x)
(b) \(\frac{1}{f(x)}\)
(c) \(-\frac{1}{f(x)}\)
(d) f(x)
Answer:
(b) \(\frac{1}{f(x)}\)
Hint:
f(x) = \(\frac{1-x}{1+x}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q4

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 5.
The graph of the line y = 3 is:
(a) Parallel to x-axis
(b) Parallel to the y-axis
(c) Passing through the origin
(d) Perpendicular to the x-axis
Answer:
(a) Parallel to x-axis
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q5

Question 6.
The graph of y = 2x2 is passing through:
(a) (0, 0)
(b) (2, 1)
(c) (2, 0)
(d) (0, 2)
Answer:
(a) (0, 0)
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q6
y = 2x2
Put x = 0, y = 0 the equation is satisfied.

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 7.
The graph of y = ex intersect the y-axis at:
(a) (0, 0)
(b) (1, 0)
(c) (0, 1)
(d) (1, 1)
Answer:
(c) (0, 1)
Hint:
y = ex
Put x = 0, we get y = e0 = 1.
∴ The graph intersects the y-axis at (0, 1)

Question 8.
The minimum value of the function f(x) = |x| is:
(a) 0
(b) -1
(c) +1
(d) ∞
Answer:
(a) 0
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q8
f(x) = |x|
f(0) = |0| = 0

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 9.
Which one of the following functions has the property f(x) = f(\(\frac{1}{x}\))?
(a) f(x) = \(\frac{x^{2}-1}{x}\)
(b) f(x) = \(\frac{1-x^{2}}{x}\)
(c) f(x) = x
(d) f(x) = \(\frac{x^{2}+1}{x}\)
Answer:
(d) f(x) = \(\frac{x^{2}+1}{x}\)
Hint:
f(x) = f(\(\frac{1}{x}\))
take f(x) = \(\frac{x^{2}+1}{x}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q9

Question 10.
If f(x) = 2x and g(x) = \(\frac{1}{2^{x}}\) then (fg)(x) is:
(a) 1
(b) 0
(c) 4x
(d) \(\frac{1}{4^{x}}\)
Answer:
(a) 1
Hint:
(fg) x = f(x) g(x) = \(2^{x} \times \frac{1}{2^{x}}\) = 1

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 11.
Which of the following function is neither even nor odd?
(a) f(x) = x3 + 5
(b) f(x) = x5
(c) f(x) = x10
(d) f(x) = x2
Answer:
(a) f(x) = x3 + 5
Hint:
Since it has a constant term 5.
f(x) = x3 + 5
f(-x) = (-x)3 + 5 = -x3 + 5.
It is not either f(x) or -f(x).

Question 12.
f(x) = -5, for all x ∈ R is a:
(a) an identity function
(b) modulus function
(c) exponential function
(d) constant function
Answer:
(d) constant function

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 13.
The range of f(x) = |x|, for all x ∈ R is:
(a) (0, ∞)
(b) [0, ∞)
(c) (-∞, ∞)
(d) [1, ∞)
Answer:
(b) [0, ∞)
Hint:
[0, ∞) since in this interval 0 is included and f(0) = 0.

Question 14.
The graph of f(x) = ex is identical to that of:
(a) f(x) = ax, a > 1
(b) f(x) = ax, a < 1
(c) f(x) = ax, 0 < a < 1
(d) y = ax + b, a ≠ 0
Answer:
(a) f(x) = ax, a > 1

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 15.
If f(x) = x2 and g(x) = 2x + 1 then (fg)(0) is:
(a) 0
(b) 2
(c) 1
(d) 4
Answer:
(a) 0
Hint:
(fg)(0) = f(o) g(o)
= 02 (2(0) + 1)
= 0(1)
= 0

Question 16.
\(\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}=\)
(a) 1
(b) ∞
(c) -∞
(d) θ
Answer:
(a) 1 (By formula)

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 17.
\(\lim _{x \rightarrow 0} \frac{e^{x}-1}{x}=\)
(a) e
(b) nxn-1
(c) 1
(d) 0
Answer:
(c) 1 (By formula)

Question 18.
For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?
(a) -2
(b) 1
(c) 2
(d) -1
Answer:
(b) 1
Hint:
When x = 1, \(\frac{x+2}{x-1}\) is not defined.

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 19.
A function f(x) is continuous at x = a \(\lim _{x \rightarrow a} f(x)\) is equal to:
(a) f(-a)
(b) f(\(\frac{1}{a}\))
(c) 2f(a)
(d) f(a)

Question 20.
\(\frac{d}{d x}\left(\frac{1}{x}\right)\) is equal to:
(a) \(-\frac{1}{x^{2}}\)
(b) \(-\frac{1}{x}\)
(c) log x
(d) \(\frac{1}{x^{2}}\)
Answer:
(a) \(-\frac{1}{x^{2}}\)

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 21.
\(\frac{d}{d x}\) (5ex – 2 log x) is equal to:
(a) 5ex – \(\frac{2}{x}\)
(b) 5ex – 2x
(c) 5ex – \(\frac{1}{x}\)
(d) 2 log x
Answer:
(a) 5ex – \(\frac{2}{x}\)
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q21

Question 22.
If y = x and z = \(\frac{1}{x}\) then \(\frac{d y}{d z}\) =
(a) x2
(b) 1
(c) -x2
(d) \(\frac{-1}{x^{2}}\)
Answer:
(c) -x2
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q22

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 23.
If y = e2x then \(\frac{d^{2} y}{d x^{2}}\) at x = 0 is:
(a) 4
(b) 9
(c) 2
(d) 0
Answer:
(a) 4
Hint:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10 Q23

Question 24.
If y = log x then y2 =
(a) \(\frac{1}{x}\)
(b) \(-\frac{1}{x^{2}}\)
(c) \(-\frac{2}{x^{2}}\)
(d) e2
Answer:
(b) \(-\frac{1}{x^{2}}\)
Hint:
y = log x
∴ y1 = \(\frac{1}{x}\)
∴ y2 = \(\frac{-1}{x^{2}}\)

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.10

Question 25.
\(\frac{d}{d x}\left(a^{x}\right)=\)
(a) \(\frac{1}{x \log _{e} a}\)
(b) aa
(c) x logea
(d) ax logea
Answer:
(d) ax logea (by formula)

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