Evaluate lim t rightarrow 0 sin4tt Evaluate lim x rightarrow

Evaluate: lim t rightarrow 0 sin4t/t Evaluate: lim x rightarrow 3 4x + 3x2/3 - x Find the derivative by the limit process: g(x) = 3 - 4x2. Write the equation of the tangent line to the graph of y = x + 4/x - 4 at the point (2, - 3). Do not simplify. Find the derivative: f(t) = + 6 - 4e2t

Solution

2) lim 4 sin(4t) / (4t) = 4 ANSWER
x->0
4) y= (x+4) /(x-4) at (2,-3) , x=2
y\' = -(8/(-4 + x)^2)
slope =m =y\'(2) -8 / (-4+2) = -8 / 4= -2

y-yo= m(x-x0)
y+3 = -2 (x-2) tangent line

5) f(t) = t^(1/4) + 6 - 4 e^(2t)
f \' (t) = (1/4) t^( (1/4) -1) + 0 - 8 e^(2t)

f \' (t) = (1/4) t^( -3/4) - 8 e^(2t)