hi i would like the same expert to do this becausethey need to match the same kind writingand paper used when they submitthe pictures of the solution or they will notice the differencein the writing...

HW 4.2
1)
2)
3)
     
     
     
     
     
    Actual value
    x
    f(x)
    I order
    II order
    III order
     
    2
    e^x
    3
    5
    6.5
    7.389056
    2
    sinx
    2
    2
    0.666667
    0.9093
    2
    cosx
    1
    1
    -1
    -0.4161
We find that when we increase the order the value we get from series is closer to actual value.
    
    
    
    
    
    Actual value
    x
    f(x)
    I order
    II order
    III order
     
    0.001
    e^x
    1.001
    1.001001
    1.001001
    1.001001
    0.001
    sinx
    0.001
    0.001
    0.001
    0.001
    0.001
    cosx
    1
    1
    1
    1
    
    
    
    
    
    Actual value
    x
    f(x)
    I order
    II order
    III order
     
    0.01
    e^x
    1.01
    1.01005
    1.01005
    1.01005
    0.01
    sinx
    0.01
    0.01
    0.01
    0.01
    0.01
    cosx
    1
    0.99995
    0.99995
    0.99995
Thus when we take x very close to 0 we get more accurate values
Hence when x is very close to a, and when we consider a higher degree polynomial, error is minimum.
6)...