Calculus

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Q. 1. Find the derivative of f(x) = (1+x)(1+x2) (1+x4) (1+x8), and hence find f ¢ (1)

Q. 2. If Q. 3. Differentiate w.r.t.x

find

Q. 4. Differentiate y = ax + xa + aa + xx w.r.t.x. Q. 5. Differentiate Q. 6. Differentiate w.r.t.x w.r.t.x for x>0, a>0.

Q. 7. Differentiate Q. 8. Find

w.r.t.x

Q. 9.

Q. 10. Prove that

Q. 11. If

Show that Q. 12. If

Q. 13. If

Q. 14. If

Q. 15. Find

if

Q. 16. Find

if y = x log (logx)

Q. 17. If x = a(cos q + qsinq), y =a(sin q -qcosq), find

Q. 18. If Sin y = x sin ( a + y ) , with Cos a ≠ 1, P.T

Q. 19. Find

, if x =

Q. 20. If Q. 21. If y = acos(logx) +bsin(logx). S.T.x2y2+xy1+y=0. , Prove that (1+x2)2y2 +2x((1+x2)y1 = 2. , show that (1+x2 ) y2+(2x-1)y1=0.

Q. 22. If y = Q. 23. If

Q. 24. If Q. 25. If Q. 26. If

, show that

(1-x2 )y2 -xy1 = 0 , show that (1-x2 )y2 -xy2 -a2y =0 .

show that (1-x2 )y2 -xy1-m2y =0 .

Q. 27. If y = 3e2x+2e3x, then prove that y2-5y1+6y=0 Q. 28. If (x-a)2 +(y-b)2 = c2 ,for some c>0. prove that

is a constant, independent of a and b .

Q. 29. If x =sint, y = sinpt. Show that Q. 30. If y = sin . S.T. (1-x2)y2-xy1+ m2y =0.

Q. 1. Discuss the continuity of

Q. 2. If

Q. 3. Differentiate the following function w.r.t. x….

Q. 4. If

then show that

Q. 5.

Q. 6. Differentiate

with respect to

Q. 7. If

show that

Q. 8. Find the value of a and b such that the function defined by

Q. 1. Discuss the continuity of

Q. 2. Find the relationship between a and b so that the function f defined by

Q. 3. If

then show that

Q. 4. Q. 5.If cos y = x Cos (a + y), with

prove that

Q. 6. Differentiate Q. 7.

w.r.to x.

Q. 8. If

for some c > 0, prove that

is a constant independent of a and b. Q. 1. Discuss the continuity of

Q. 2. For what value of

is the function defined by

continuous at x = 0? What about continuity at x = 1? Q. 3.

Q. 4.

Q. 5.

Q. 6.

Q. 7.

Q. 8.

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