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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.3

Question 1.

(a) Find the left right limits of f(x) = \(\frac{x^{2}-4}{\left(x^{2}+4 x+4\right)(x+3)}\) at x = -2

(b) f(x) = tan x at x = \(\frac{\pi}{2}\)

Solution:

(a) f(x) = \(\frac{x^{2}-4}{\left(x^{2}+4 x+4\right)(x+3)}\) at x → -2

Evaluate the following limits

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

f(x) → ∞ as x → ∞

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

An important problem in fishery science is to estimate the number of fish presently spawning in streams and use this information to predict the number of mature fish or “recruits” that will return to the rivers during the reproductive period. If S is the number of spawners and R the number of recruits, “Beverton-Holt spawner recruit function” is R(S) = \(\frac{S}{(\alpha S+\beta)}\) where α and β are positive constants. Show that this function predicts approximately constant recruitment when the number of spawners is sufficiently large.

Solution:

Question 10.

A tank contains 5000 litres of pure water. Brine (very salty water) that contains 30 grams of salt per litre of water is pumped into the tank at a rate of 25 litres per minute. The concentration of saltwater after t minutes (in grams per litre) is C(t) = \(\frac{30 t}{200+t}\). What happens to the concentration as t → ∞?

Solution:

### Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.3 Additional Problems

Question 1.

Evaluate

Solution:

The given expression is of the form ∞ – ∞. So we first write it in the rational form \(\frac{f(x)}{g(x)}\). So that it reduces to either \(\frac{0}{0}\) form or \(\frac{\infty}{\infty}\) form.

Question 2.

Evaluate:

Solution:

Here the expression assumes the form ∞ – ∞ as x → ∞. So, we first reduce it to the rational form \(\frac{f(x)}{g(x)}\)

Question 3.

Evaluate

Solution:

We have

Question 4.

Evaluate:

Solution:

We have,

Question 5.

Evaluate:

Solution:

Question 6.

Evaluate:

Solution: