1. Use the first five terms of the exponential series of e^x and a calculator to approximate e^1.2 to the nearest hundredth.

Question

I have no idea how to solve these problems, so steps would be helpful...

The answer choices are the following for number 1...

A) e^12= 1 + 1.2 + 1.44/2 + 1.728/6 + 2.0736/24 = 3.29
B) e^12= 1 + 1.2 + 1.728/6 + 2.0736/24 = 3.29
C) e^12= 1.2 + 1.44/2 + 1.728/6 + 2.0736/24 = 3.29
D) e^12= 1 + 1.44/2 + 1.728/6 + 2.0736/24 = 3.29

2. Use the first five terms of the trigonometric series to approximate the value of sin 6pi/15 to four decimal places. Then compare the approximation to the actual value.

A) -0.9568, -0.9659
B) -0.9649, -0.9659
C) -0.9609, -0.9659
D) 0.9511, 0.9511

3. Find ln (-67.7).
A) i pi + 5.2151
B) i pi + 6.2151
C) i pi + 4.2151
D) i pi - 7.2151

Answer 1

The Maclaurin Series for e^x is 1 + x + x²/2! + x³/3! + ...

 

So, using the first 5 terms,

 

      e^1.2 ≈ 1 + 1.2 + (1.2)²/2! + (1.2)³/3! + (1.2)⁴/4!

Answer 2

The question asking to find ln(-67.7) is asking the impossible because ln(x) requires x > 0.

 

Question 1 appears to have a mistake; the proposed answers all should be e^(1.2), judging by the various terms on the right side, i.e. e^x = 1 + x + x²/2! + x³/3!+...  this is not e^(12) ... MISSING DEC. POINT in arguments.