Question

Use linear Approximation to approximate e^.01

Answer 1

ah a relic from the days when you could just whip out a $8 calculator and plug it in

Answer 2

which, btw, is exactly what i would do!

Answer 3

f(x)=e^x
we need to find a tangent line close to x=0.01
x=0 is pretty close
f(0)=e^0=1 <-(0,1) oour point of tangency
f'(x)=e^x
f'(0)=e^0=1 <- this is slope=m
y=mx+b
y=1x+b
we know a point on the line (0,1)
1=1*0+b
1=b
y=1x+1
or
y=x+1
so we can estimate
e^.01
by pluging 0.01 into our linear approximation
f(x) apprx=0.01+1=1.01