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CBSE CLASS XII

Continuity & Differentiation

Q. 1. Find the values of a and b such that the function defined by

f(x) = ( 5, if x £ 2
ax + b if 2<x<10
21, if x  10 ) is a continuous function 
Q. 2. Find sin²y + cos (xy) = p

Q. 3. Differentiate w.r.t. x (x cosx)^x + (x sinx)^1/x

Q. 4. If x = , = show that

Q. 5. If y = (tan^-1x)² show that

& (x² + 1)² y² + 2x (x²+ 1) y1 = 2.
Q. 6. Differentiate sin^-1w.r.t. x

Q. 7. If x for -1<x<1, show that

Q. 8. Find if y = a t + 1/t x = ( t + 1/t)a

Q. 9. Discuss the continuity of the function given by:-
f(x) = |x - 1| + |x - 2| at x = , and x = 2

Q. 10. If the function f(x) is given by   f(x) =  { 3ax + b) if x>1if  x = 1(5ax – 2b if  x<1}
is continuous at  x = 1, find the values of  a and b.
Q. 11. If  y = [x + ]ⁿ, then prove that

Q. 12. Prove :  

Q. 13. Find when y =  sec^-1

Q. 14. If ex + ey = ex+y prove that 

Q. 15. Given that cos-------------------= prove that

Q. 16. If x=a(q + sinq), y= a(1+ cosq), prove that

Prepared By Anil Kumar Tondak
M.Sc.(Maths), M.Ed., M.A.(Eco),M.B.A.(Mkt)
Mob No. 9811363962