Let `g(x)|f(x+c)f(x+2c)f(x+3c)f(c)f(2c)f(3c)f^(prime)(c)f^(prime)(2c)f^(prime)(3c)|,` where `c` is constant, then find `(lim)_(xvec0)(g(x))/x`

"Let "g(x)=|{:(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|, where c is constant, then find lim_(xrarr0) (g(x))/(x).

"Let "g(x)=|{:(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|, where c is constant, then find lim_(xrarr0) (g(x))/(x).

If g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c))|, where c is a constant, then lim_(x rarr0)(g(x))/(x) is equal to

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

Write the value of lim_(x->c)(f(x)-f(c))/(x-c) .

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g^('')(f(x)) equals. (a) -(f^('')(x))/((f^'(x))^3) (b) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^3)/(f^(prime)(x)) (c) (f^(prime)(x)f^('')(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2) (d) none of these

If (lim)_(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of (lim)_(x->c)f(x) .

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

Suppose f and g are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all x and f^(prime) and g' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x)) is equal (a) (-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c) (-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

If f is a continuous function on [0,1], differentiable in (0, 1) such that f(1)=0, then there exists some c in (0,1) such that cf^(prime)(c)-f(c)=0 cf^(prime)(c)+cf(c)=0 f^(prime)(c)-cf(c)=0 cf^(prime)(c)+f(c)=0