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Exercise 5.7 - Chapter 5 Continuity & Differentiability class 12 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6990/Chapter%205_html_m7a59faf5.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6990/Chapter%205_html_41f03fdb.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6990/Chapter%205_html_140e559d.gif

Question 2:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6991/Chapter%205_html_m2468ff53.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6991/Chapter%205_html_m7bd30f86.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6991/Chapter%205_html_m57b41e71.gif

Question 3:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6992/Chapter%205_html_m23f4c69b.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6992/Chapter%205_html_2aec51b6.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6992/Chapter%205_html_71a5f565.gif

Question 4:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6993/Chapter%205_html_727b0d3e.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6993/Chapter%205_html_m5d5bb1c3.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6993/Chapter%205_html_4c379a84.gif

Question 5:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6994/Chapter%205_html_33c4eae6.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6994/Chapter%205_html_m34818b33.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6994/Chapter%205_html_192f1554.gif

Question 6:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6995/Chapter%205_html_480384f8.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6995/Chapter%205_html_m338bf3ed.gif

Then, https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6995/Chapter%205_html_mf68e5a3.gif

Question 7:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6996/Chapter%205_html_47bf6e60.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6996/Chapter%205_html_6f6eedb7.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6996/Chapter%205_html_m72401aa9.gif

Question 8:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6997/Chapter%205_html_6b1d3f6d.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6997/Chapter%205_html_m5f1b07e9.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6997/Chapter%205_html_m1e4696a0.gif

Question 9:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6998/Chapter%205_html_f8f0eb6.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6998/Chapter%205_html_6451572a.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6998/Chapter%205_html_m49c47554.gif

Question 10:

Find the second order derivatives of the function.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6999/Chapter%205_html_m4ebb87cd.gif

Answer:

Lethttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6999/Chapter%205_html_5f4c3a91.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/6999/Chapter%205_html_203b096f.gif

Question 11:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7000/Chapter%205_html_m287fb11e.gif , prove thathttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7000/Chapter%205_html_m2b67ca89.gif

Answer:

It is given that,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7000/Chapter%205_html_m287fb11e.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7000/Chapter%205_html_4a272fe7.gif

Hence, proved.

Question 12:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7001/Chapter%205_html_m7285ceb0.gif  findhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7001/Chapter%205_html_48519442.gif in terms of y alone.

Answer:

It is given that,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7001/Chapter%205_html_27f47e6b.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7001/Chapter%205_html_500433ae.gif

Question 13:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7002/Chapter%205_html_6a6aad23.gif , show thathttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7002/Chapter%205_html_m6fb302b5.gif

Answer:

It is given that,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7002/Chapter%205_html_6a6aad23.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7002/Chapter%205_html_m1d04d99e.gif

Hence, proved.

Question 14:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7003/Chapter%205_html_3538e479.gif show thathttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7003/Chapter%205_html_mdce2140.gif

Answer:

It is given that,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7003/Chapter%205_html_m3ce836af.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7003/Chapter%205_html_m1a6b17e8.gif

Hence, proved.

Question 15:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7005/Chapter%205_html_m173671fd.gif , show thathttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7005/Chapter%205_html_m61d13575.gif

Answer:

It is given that,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7005/Chapter%205_html_m173671fd.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7005/Chapter%205_html_m12fbda7f.gif

Hence, proved.

Question 16:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7006/Chapter%205_html_m1f2a0c9e.gif , show thathttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7006/Chapter%205_html_m365ab33e.gif

Answer:

The given relationship ishttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7006/Chapter%205_html_m1f2a0c9e.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7006/Chapter%205_html_4513d279.gif

Taking logarithm on both the sides, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7006/Chapter%205_html_m7a51c783.gif

Differentiating this relationship with respect to x, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7006/Chapter%205_html_4686e8e2.gif

Hence, proved.

Question 17:

Ifhttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7007/Chapter%205_html_362aaa15.gif , show thathttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7007/Chapter%205_html_m616df3d0.gif

Answer:

The given relationship ishttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7007/Chapter%205_html_362aaa15.gif

Then,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/234/7007/Chapter%205_html_m10ec30e3.gif

Hence, proved.

Also Read : Exercise-5.8-Chapter-5-Continuity-&-Differentiability-class-12-ncert-solutions-Maths

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