This set of Engineering Mathematics Quiz focuses on “Taylor Mclaurin Series – 4”.

1. The expansion of f(x), about x = a is

View Answer

Explanation: By taylor expansion,

f(a+h) = f(a) +

^{h}⁄

_{1!}f’ (a) +

^{h2}⁄

_{2!}f

^{”}(a)…….

2. Find the expansion of e^{x} in terms of x + m, m > 0.

View Answer

Explanation: Let, h = x + m = > f(x) = f(h-m) = e

^{(h-m)}

By taylor theorem, putting a = -m , we get,

3. Expand ln(x) in the power of (x-m).

View Answer

Explanation: where, h = x-m

Let, h = x – m => f(x) = f(h+m) = e

^{(h+m)}

By taylor theorem, putting a = m , we get,

4. Find the value of √10

a) 3.1633

b) 3.1623

c) 3.1632

d) 3.1645

View Answer

5. Expand f(x) = ^{1}⁄_{x} about x = 1.

a) 1 – (x-1) + (x-1)^{2} – (x-1)^{3} +⋯….

b) 1 + (x-1) + (x-1)^{2} + (x-1)^{3} +⋯….

c) 1 + (x-1) – (x-1)^{2} + (x-1)^{3} +⋯….

d) 1 – (x+1) + (x+1)^{2} – (x+1)^{3} +⋯….

View Answer

Explanation: Given f(x) =

^{1}⁄

_{x}

Let, x – 1 = h

Hence, x = 1 + h

Hence, f(x) = f(1 + h) = f(1) + ^{h}⁄_{1!} f’ (1) + ^{h2}⁄_{2!} f^{”} (1) +^{h3}⁄_{3!} f^{”’} (1)+⋯…

Now, f(1) = 1, f'(1) = -1, f”(1) = 2 ,f”'(1) = -6,…….

Hence, f(1 + h) = 1 – h + h^{2} – h^{3}+⋯…

hence, 1 – (x-1) + (x-1)^{2} – (x-1)^{3} +⋯….

6. Find the expansion of f(x) = ^{ex} ⁄_{1+ex}, given ∫f(x)dx = ln(2), for x = 0

View Answer

7. Find the value of e^{π⁄4√2}

a) 1.74

b) 1.84

c) 1.94

d) 1.64

View Answer

8. Find the value of ln(sin(31^{o})) if ln(2) = 0.69315

a) -0.653

b) -0.663

c) -0.764

d) -0.662

View Answer

9. The expansion of f(x,y), is

View Answer

10. The expansion of f(x, y)=e^{x Sin(y)}, is

a) x + xy + ……..

b) y + y^{2} x + ……..

c) x + x^{2} y + ……..

d) y + xy + ……..

View Answer

Explanation: Now, f(x, y)=e

^{x Sin(y)}, f(0,0) = 0

Therefore,

f

_{x}(x,y) = e

^{x}Sin(y), hence f

_{x}(0,0) = 0

f_{y} (x,y) = e^{x} Cos(y), hence f_{y} (0,0) = 1

f_{xx} (x,y) = e^{x} Sin(y), hence f_{xx} (0,0) = 0

f_{yy} (x,y) = -e^{x} Sin(y), hence f_{yy} (0,0) = 0

f_{xy} (x,y) = e^{x} Cos(y), hence f_{xy} (0,0) = 1

By taylor expansion,

f(x,y) = 0 + 0 + y + ^{1}⁄_{2}! [0 + 2xy + 0] +⋯.

f(x,y) = y + xy + ……..

11. The expansion of f(x, y) = e^{x} ln(1 + y), is

a) f(x,y)= y + xy – ^{y2}⁄_{2} +…….

b) f(x,y)= y – xy + ^{y2}⁄_{2} -…….

c) f(x,y)= y + x – ^{y2}⁄_{2} +……..

d) f(x,y)= x + y – ^{x2}⁄_{2} +……..

View Answer

**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

To practice all areas of Engineering Mathematics for Quizzes, __here is complete set of 1000+ Multiple Choice Questions and Answers__.