Question

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = ln(1 + 4x)
What is the sum in sigma notation and what is the R
Thanks

Answer 1

Answer:

Maclaurin series for f(x) using the definition of a Maclaurin series.

[Assume that f has a power series expansion.

Do not show that Rn(x) → 0.]

f(x) = ln(1 + 4x)

Answer 2

Answer:

Given:

Height of triangular prism = 10 cm

Sides of base = 3, 4, 5 cm

To find:

Total surface area of prism = ?

Solution:

First of all, let us have a look at the formula for Total Surface Area of triangular prism:

TSA = B + p\times hTSA=B+p×h

Where B is the area of base

p is the perimeter of base and

h is the height of prism.

here base is a right angled triangle (because 3, 4, 5 is a triplet) Base and Height will be 3 , 4 cm or 4, 3 cm and 5 will be hypotenuse.

So formula for B:

\begin{gathered}B = \dfrac{1}{2}\times Base \times Height\\B = \dfrac{1}{2}\times 3\times 4 = 6 cm^2\end{gathered}

B=

2

1

×Base×Height

B=

2

1

×3×4=6cm

2

So, TSA = 6 + (3+4+5) \times× 10 = 6 + 120 = 126 cm^2cm

2

So, total surface area of given prism is 126cm^2cm

2

.