Find the values of `aa n db` if `f(x)={a x^2+1,xlt=1x^2+a x+b ,x >1i sd iffe r e n t i a b l ea tx=1`

Find the values of aa n db if f(x)={a x^2+1,xlt=1 ,x^2+a x+b ,x >1"i s differentiable at"x=1

Find the values of aa n db if f(x)={a+sin^(-1)(x+b), xgeq1 and x ,x<1 is differentiable at x=1.

Find the values of aa n db such that int(dx)/(1+sinx)=tan(x/2+a)+b

If f(x)={x ,xlt=1,x^2+b x+c ,x >1' find b and c if function is continuous and differentiable at x=1

Find the values of a if f(x)=("lim")_(n rarr oo)(a x^(2n)+2)/(x^(2n)+a+1) is continuous at x=1.

If the function f(x)={A x-B ,xlt=1 3x ,1

If the function f(x)={A x-B ,xlt=1 3x ,1

Which of the following function is/are periodic? (a)f(x)={1,xi sr a t ion a l0,xi si r r a t ion a l (b)f(x)={x-[x]; 2n

Find the number of polynomials of the form x^3+a x^2+b x+c that are divisible by x^2+1,w h e r ea , b ,c in {1,2,3,9,10}dot

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, (a) f(x)h a sr a ngZ (b) f(x)i sp e r iod i c function (c) f(x)i sin v e r t i b l ein[0,pi/4] (d) f(x) is into function