The approximate value of e^-0.01 is 0.99
Given :
we use linear approximation to estimate the given number
[tex]e^{-0.01}[/tex]
For linear approximation we use equation
[tex]L(x)=f(a)+f'(a)(x-a)[/tex]
Lets assume some value for 'a' that is close to -0.01
Lets assume a=0
[tex]f(x)=e^x\\f(0)=e^0\\f'(x)=e^x\\f'(0)=e^0[/tex]
Lets plug in all the values
[tex]L(x)=f(a)+f'(a)(x-a)\\L(x)=e^0+e^0(x-0)\\L(x)=1+1(x-0)\\L(x)=1+1x[/tex]
Now we estimate e^-0.01
the value of x is -0.01
[tex]L(x)=1+x\\L(-0.01)=1-0.01\\L(-0.01)=0.99[/tex]
The approximate value is 0.99
Learn more : brainly.com/question/2111949
