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`

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is

Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AAx , y in R and g^(prime)(0)=aa n dg^(prime)(3)=bdot Then find the value of g^(prime)(-3)dot

Evaluate: ("lim")_(xvec0)(1-cos2x)/(x^2)

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) for all x!=0, then find the value of ("lim")_(xvec0)f(x)

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

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_______