2nd PUC Maths Question Bank Chapter 5 Continuity and Differentiability Ex 5.7

Students can Download Maths Chapter 5 Continuity and Differentiability Ex 5.7 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 5 Continuity and Differentiability Ex 5.7

2nd PUC Maths Continuity and Differentiability NCERT Text Book Questions and Answers Ex 5.7

Find the second order derivatives of the functions given in Exercises 1 to 10.

Question 1.
x² + 3x + 2
Answer:

Question 2.
x²⁰
Answer:

Question 3.
x. cos x
Answer:

Question 4.
log x
Answer:

Question 5.
x³ log x
Answer:

Question 6.
e^x sin 5x
Answer:

Question 7.
e^6x cos 3x
Answer:

Question 8.
tan^-1 x
Answer:

Question 9.
log  (log x)
Answer:

Question 10.
sin(log x)
Answer:

Question 11.
If y = 5 cos x – 3 sin x prove that \(\frac{d^{2} y}{d x^{2}}+y=0\)
Answer:

Question 12.
\(\text { If } y=\cos ^{-1} x, \text { Find } \frac{d^{2} y}{d x^{2}}\)
in terns of y alone
Answer:

Question 13.
If y = 3 cos (log x) + 4 sin (log x), show that x²y₂ + xy₁ + y = 0
Answer:

Question 14.
If y = Ae^-nx + Be^nx, Show that
\(\frac{d^{2} y}{d x^{2}}-(m+n) \frac{d y}{d x}+m n y=0\)
Answer:

Question 15.
If y = 500e^7x + 600e^-7x, show that \(\frac{d^{2} y}{d x^{2}}=49 y\)
Answer:

Question 16.
\(\text { If } \mathrm{e}^{y}(x+1)=1, \text { show that } \frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}\)
Answer:

Question 17.
If y = (tan^-1 x)², show that (x² + 1)² y₂ + 2x (x² + 1) y₁ = 2
Answer: