Students can download 11th Business Maths Chapter 5 Differential Calculus Ex 5.2 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 5.2

Samacheer Kalvi 11th Business Maths Differential Calculus Ex 5.2 Text Book Back Questions and Answers

Question 1.
Evaluate the following:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q11
Solution:
(i) \(\lim _{x \rightarrow 2} \frac{x^{3}+2}{x+1}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1

(ii) \(\lim _{x \rightarrow \infty} \frac{2 x+5}{x^{2}+3 x+9}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.1
[Takeout x from numerator and take x2 from the denominator]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.2

(iii) \(\lim _{x \rightarrow \infty} \frac{\Sigma n}{n^{2}}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.3

(iv) \(\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{5 x}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.4

(v) \(\lim _{x \rightarrow a} \frac{x^{\frac{5}{8}}-a^{\frac{5}{8}}}{x^{\frac{2}{3}}-a^{\frac{2}{3}}}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.5
[Divide both numerator and denominator by x – a; \(\lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x-a}=n a^{n}\)]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.6

(vi) \(\lim _{x \rightarrow 0} \frac{\sin ^{2} 3 x}{x^{2}}\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q1.7

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2

Question 2.
If \(\lim _{x \rightarrow a} \frac{x^{9}-a^{9}}{x-a}=\lim _{x \rightarrow 3}(x+6)\), find the value of a.
Solution:
\(\lim _{x \rightarrow a} \frac{x^{9}-a^{9}}{x-a}=\lim _{x \rightarrow 3}(x+6)\)
9 . a9-1 = 3 + 6
9 . a8 = 9
a8 = 1
Taking squareroot on bothsides, we get
\(\left(a^{8}\right)^{\frac{1}{2}}\) = ±1
a4 = ±1
But a4 = -1 is imposssible.
∴ a4 = 1
Again taking squareroot, we get
\(\left(a^{4}\right)^{\frac{1}{2}}\) = ±1
a2 = ±1
a2 = -1 is imposssible
∴ a2 = 1
Again taking positive squareroot, a = ±1

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2

Question 3.
If \(\lim _{x \rightarrow 2} \frac{x^{n}-2^{n}}{x-2}=448\), then find the least positive integer n.
Solution:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q3
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q3.1

Question 4.
If f(x) = \(\frac{x^{7}-128}{x^{5}-32}\), then find \(\lim _{x \rightarrow 2} f(x)\)
Solution:
\(\lim _{x \rightarrow 2} f(x)\)
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q4

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2

Question 5.
Let f(x) = \(\frac{a x+b}{x+1}\), if \(\lim _{x \rightarrow 0} f(x)=2\) and \(\lim _{x \rightarrow \infty} f(x)=1\), then show that f(-2) = 0
Solution:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q5
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.2 Q5.1
Hence Proved.

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