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(I) Differentiate the following w.r.t. x Question 1. Solution: Question 2.y = √x + tan x – x3Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: (II) Diffrentiate the following w.r.t. x Question 1.y = x5 tan xSolution: Question 2.y = x5 log xSolution: Question 3.y = (x2 + 2)2 sin xSolution: Question 4.y = … Read more

Question 1.Find the derivatives of the following w.r.t. x by using the method of the first principle. By first principle, we get (b) sin(3x)Solution:Let f(x) = sin 3xf(x + h) = sin3(x + h) = sin(3x + 3h)By first principle, we get (c) e2x+1Solution: (d) 3xSolution: (e) log(2x + 5)Solution:Let f(x) = log(2x + 5)∴ … Read more

(I) Select the correct answer from the given alternatives. Question 1. Hint: Question 2. Hint: Question 3.Hint: Question 4. (A) f is discontinuous at x = 2(B) f is discontinuous at x = -4(C) f is discontinuous at x = 0(D) f is discontinuous at x = 2 and x = -4Answer:(B) f is discontinuous … Read more

Question 1.Examine the continuity of(i) f(x) = x3 + 2 x2 – x – 2 at x = -2Solution:Given, f(x) = x3 + 2 x2 – x – 2f(x) is a polynomial function and hence it is continuous for all x ∈ R.∴ f(x) is continuous at x = -2. Solution: = 8 for x = 3, at x … Read more

I. Select the correct answer from the given alternatives. Question 1. (A) 23(B) 32(C) -32(D) -16Answer:(C) -32Hint: Question 2. Hint: Question 3. Hint: Question 4. Hint: Question 5. Hint: Question 6. (A) 0(B) 1(C) 2(D) 3Answer:(C) 2Hint: Question 7.Hint: Question 8. (A) log 15(B) log 3 + log 5(C) log 3 . log 5(D) 3 … Read more

I. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: II. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: III. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution:

I. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: II. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: III. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question … Read more

I. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: II. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution:

I. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: II. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: III. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution:

I. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: II. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: III. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question … Read more