use Newton’s forward and backward Interpolation formula

1.    Find the value of e^1.85 given

e^1.7=5.4739, e^1.8= 6.0496, e^1.9= 6.6859, e^2.0=7.3891, e^2.1=8.1662, e^2.2=9.0250, e^2.3= 9.9742.

2.    Find the value of y at x=1.05 from the table given below:

X       1.0    1.1    1.2    1.3    1.4    1.5

Y        .841  .891  .932  .964  .985  1.015

3.    Find  the value of f(1.02) given the following data

X                 f(x)

1.0              1.841

1.1              1.891

1.2              0.932

1.3              0.964

1.4              0.985

4.    Find y at x= 105 from the following data:

X                 y

80               5026

85               5674

90               6362

95               7088

100             7854

5.    Find log π given π=3.14159 and

Log 3.141 = 0.4970679364

Log 3.142=0.4972061807

Log3.143=0.4973443810

Log 3.144=0.4974825374

Log 3.145=0.4976206498

6.    Find y(1.02) given

X                 y

1.00            0.3413

1.05            0.3531

1.10            0.3643

1.15            0.3749

1.20            0.3849

7.    Find the value of y at x= 9

X                 y

2                 94.8

5                 87.9

8                 81.3

11               75.1

8.    From the following table estimate sin 28®24’

Ф                 sin ф

25               0.42262

26               0.43837

27               0.45399

28               0.46947

29               0.48481

30               0.50000

9.    Estimate e^-1.9 from the given data

X                 e^-x

1.00            0.3679

1.25            0.2865

1.50            0.2231

1.75            0.1738

2.00            0.1353

10.                       Find f(0.5) if f(-1)=202, f(0)=175, f(1)=82 and f(2)=55