Solve the below:
Find the derivative;
G(v)= (v^3-1)/(v^3+1)
Find the limit;
lim(sin3x)/(sin5x)
x->0
Find the derivative;
R(w)= (cosw)/(1-sinw)
H(o)=(1+seco)/(1-seco)
Find the derivative;
F(x)= cos(3x^2)+{cos^2}3x
N(x)=(sin5x-cos5x)^5
"Assume that the equation determines a differentiable function f such that y=f(x), find y'."
5x^2-xy-4y^2=0
x^4+4x^2y^2-3xy^2+2x=0
"Assume all variables are functions of t."
If S=z^3 and dz/dt=-2 when z=3, find dS/dt.
Find the extrema of f on the given interval.
f(x)=3x^2-10x+7; [-1,3]
"Show that f satisfies the hypotheses of Rolle's Theorem on [a,b] and find all numbers c in (a,b) such that f'(c)=0."
f(x)=5-12x-2x^2; [-7,1]
"Determine whether f satisfies the hypotheses of the mean value theorem on [a,b] and if so, find all numbers c in (a,b) such that f(b)-f(a)=f'(c)(b-a)."
f(x)=3x^2+x-4; [1,5]
Find the extrema and sketch the graph of f.
f(x)=(2x-5)/(x+3)