If `y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5,` then the value of `(a^2)/(b^2)` is_______

If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1)a n d(dy)/(dx)=a x+b , then the value of a+b is (a) cot(pi/8) (b) cot(pi/12) (c) tan((5pi)/12) (d) tan((5pi)/8)

Let z=(cosx)^5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=(2pi)/9 is____________.

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x.Also,f(3)=5 and f^(prime)(3)=4 . Then the value of [f(10)]^2-[phi(10)]^2 is _____

If b^(2)-4acle0 ("where" ane0 and a,b,c,x,y in R ) satisfies the system ax^(2)+x(b-3)+c+y=0 and ay^(2)+y(b-1)+c+3x=0 , then value of (y)/(x) is ___________.

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x)-2f^(prime)(x)-15f(x)=0 for all xdot Then the value of (|a b|)/3 is ___

The values of m for which the lines y = mx + 2 sqrt5 touches the hyperbola 16 x^(2) - 9y^(2) = 144 are the roots of x^(2) - (a+b) x-4 = 0 then the value of (a+b) is

If 4^x-2^(x+2)+5+||b-1|-3|=|siny|, x , y , b in R , then the possible value of b is_________