Plus Two Maths Chapter Wise Previous Questions Chapter 5 Continuity and Differentiability are part of Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 5 Continuity and Differentiability.

## Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 5 Continuity and Differentiability

Question 1.

a.

i. a^{x}

ii. log( a^{x} )

iii. a^{x}log a

iv. xa^{x-}^{1 }**[March-2018] **Answer:

a. iii. a

^{x}log a

b.

Question 2.

a. Prove that the function defined by f(x) = cos (x^{2}) is a continuous function.

Answer:

a. f(x) = cos(x^{2}). The domain of F is R Let g(x) = cos x and h(x) = x^{2}. Then g(x) and h(x) are continuous functions (goh) (x) = g(h(x))

= g(x^{2}) =cos(x^{2}) = f(x)

Since g and h are continuous, goh is also continuous. Hence f is continous.

Question 3.

a. Find the values of a and b such that the function

is Continous

b. Find

**[March-2017] **Answer:

Question 4.

a. Find all points of discontinuity of f, where f is defined by

b. If e^{x}‘^{y} = x^{y}, then prove that

**[March-2016]**

Answer:

Question 5.

Find

a. x^{3} + 2x^{2}y + 3xy^{2} + 4y^{3} = 5

b. x = 2 cos3 θ, y = 2 sin3 θ

c. **[March-2015] **Answer:

Question 6.

a. Find a and b if the function

is a continuous function on [-2, 2].

b. How many of the functions f(x) = |x|> g(x) =|x|^{2} and h(x) = |x|^{3} are not differentiable at x = 0?

(i) 0

(ii) 1

(iii) 2

(iv) 3 **[March-2015] **Answer:

Question 7.

a. Find the value of k if the function f(x) = kx+1 if x ≤ 5 = 3x-5 if x>5 is continuous at x= 5.

b. Find if x=a (t-sint), y=a(1+cos t).

c. Verify Rolle’s theorem for the function f(x)=x^{2}+2 in the interval [-2,2].** [March-2014] **Answer:

Question 8.

a. Consider

Find the value of k if f(x)is continuous at x=5

b. Find

c. If ,then show that

**[March-2013] **Answer:

Question 9.

Determine the value of k sothat the function

Answer:

Question 10.

a. Find the value of k if

Answer:

Question 11.

a.Check the Continuity of

b. Verify mean value theorem for f(x) =x= in [ 1,3]** [June-2011] **Answer:

Question 12.

a. Find the derivative of x^{a}+a^{x }b. Find if x=a cost; y=a sin

c. If (x+1)=1 show that

**[June-2011]**

Answer:

Question 13.

a.The function

is continuous

Find a and b?

b.

(i) Find dy \dx if y = sin x^{sinx }dx

(ii) If y = ae^{mx} + be^{nx} show that

** [March-2011]**

Answer:

Question 14.

a. Show that the function f(x)=sin (cos x) is continuous

Answer:

Question 15.

Answer:

Question 16.

a. Show that f(x) = |x| is continuous at the origin.** [March-2010] **b. Establish that g (x) = 1 – x + |x| is continuous at the origin.

c. Check whether h (x) = |1 – x + |x| is continuous at origin.

Answer:

b. 1-x is a polynomial, which is continuous at the origin. |x| is continuous at origin.

⇒ 1 – x + |x| is continuous at origin.

c. Let g (x) = 1 – x + [x| and c (x) = |x| consider (fog) x = f (g (x))

=f( 1 – x + M) = 11 = x + |x| = h (x)

Here g (x) and f (x) are continuous functions. Thus fog is continuous. Hence 11 – x+|x| is continuous at origin.

Question 17.

a. Find if

(i) y = sin(x^{3} + 7)

(ii) x = a (t – sin t); y = a (1 – cos t)

b. If y = a cos(log x) + b sin (log x);

Prove that x^{2}y_{2} + xy_{1}+ y = 0.**[March-2010] **Answer:

Question 18.

If x=a(cost+tsin t) and y=a(sint-cost)

** **Answer:

Question 19.

If (x-a)^{2}+(y-b)^{2}=c^{2 }then

Answer:

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