Another calculus question, need help.?

Question

Sketch gragp of h(x)=cosx

a. Sketch a tangent line at the point (0,1). Write a formula for the slope of the secent line joining the point (x,cosx) and (0,1)

b. Evaluate the formula for x=0.1 and x=0.01

c. Find the exact slope of the tangent line to h at the point (0,1)

d. using diritive confirm the answer

e. Find equation of the tangent line to h at the point (0,1)

Tangent Line

Answer 1

a) The tangent line is y = 1 in x,y coordinates
For "secant" line
y = mx + y0 = mx + 1
cosx = mx + 1
Thus slope is
m = (cosx - 1)/x
b) use your calculator
c) slope of tangent line is
h'(x) = dh/dx = -sinx
h'(0) = 0
d) same as c)
e) y = mx + y0, m = h', y0 = 1
y =1