Find the solution of differential equation, dy dx = xy + x2, if y = 1 at x = 0.

(1- frac{x^2}{2!}+ frac{3x^4}{4!}- frac{15x^6}{6!}+ )

( frac{x}{1!}+ frac{3x^3}{4!}+ frac{15x^5}{6!}+ )

( frac{x}{1!}- frac{3x^3}{4!}+ frac{15x^5}{6!}- )

(1+ frac{x^2}{2!}+ frac{3x^4}{4!}+ frac{15x^6}{6!}+.. )

Find the expansion of Sin(lSin-1 (x)).

(1-lx^2+ frac{l(1-l^2)}{3!} x^4- frac{l(1-l^2)(9-l^2)}{5!} x^6+ )

(lx- frac{l(1-l^2)}{3!}x^3+ frac{l(1-l^2)(9-l^2)}{5!} x^5- )

(lx+ frac{l(1-l^2)}{3!} x^3+ frac{l(1-l^2)(9-l^2)}{5!} x^5+ )

(1-lx^2+ frac{l(1-l^2)}{3!} x^4- frac{l(1-l^2)(9-l^2)}{5!} x^6+ )

(1+lx^2+ frac{l(1-l^2)}{3!} x^4+ frac{l(1-l^2)(9-l^2)}{5!} x^6+ )

Find the expansion of cos(xsin(t)).

( sum_{n=1}^ ( frac{x^n [Sin(nt)]}{n!}) )

( sum_{n=1}^ ( frac{x^n [Cos(nt)]}{n!}) )

( sum_{n=0}^ ( frac{x^n [Cos(nt)]}{n!}) )

( sum_{n=1}^ ( frac{x^n [Sin(nt)]}{n!}) )

( sum_{n=0}^ ( frac{x^n [Sin(nt)]}{n!}) )

Find the expansion of exSin(x)?

(e^{xSin(x)}=x+x^3/3+x^5/120+.. )

(e^{xSin(x)}=1+x^2-x^4/3+x^6/120- )

(e^{xSin(x)}=1+x^2+x^4/3+x^6/120+ )

(e^{xSin(x)}=x+x^3/3+x^5/120+.. )

(e^{xSin(x)}=x+x^3/3-x^5/120+ )

Find the expansion of f(x) = ln (1+ex)?

(ln u2061(2)+x/2+x^2/8+x^4/192+ . )

(ln u2061(2)+x/2+x^3/8-x^5/192+ . )

(ln u2061(2)+x/2+x^3/8+x^5/192+ . )

Expansion of y = Sin-1(x) is?

(x- frac{x^3}{6}+ frac{3}{40} x^5- frac{5}{112} x^7+ .. )

(x+ frac{x^3}{6}+ frac{3}{40} x^5+ frac{5}{112} x^7+ .. )

(x- frac{x^3}{6}+ frac{3}{40} x^5- frac{5}{112} x^7+ .. )

( frac{x^3}{6}- frac{3}{40} x^5+ frac{5}{112} x^7 .. )

(x+ frac{x^2}{6}+ frac{3}{40} x^2+ frac{5}{112} x^2+ .. )

The expansion of f(a+h) is ______

(f(a)+ frac{h}{1!} f'(a)+ frac{h^2}{2!} f (a) . )

(f(a)+ frac{h}{1!} f'(a)+ frac{h^2}{2!} f (a) .+ frac{h^n}{n!} f^n (a) )

(f(a)+ frac{h}{1!} f'(a)+ frac{h^2}{2!} f (a) . )

(hf(a)+ frac{h^2}{1!} f'(a)+ frac{h^3}{2!} f (a) .+ frac{h^n}{n!} f^n (a) )

(hf(a)+ frac{h^2}{1!} f'(a)+ frac{h^3}{2!} f (a) )

The necessary condition for the maclaurin expansion to be true for function f(x) is __________

f(x) should exists at every point

f(x) should be continuous and differentiable

Expansion of function f(x) is?

1 + x 1! f (0) + x2 2! f (0) .+xn n! fn (0)

f(0) + x 1! f (0) + x2 2! f (0) .+xn n! fn (0)

1 + x 1! f (0) + x2 2! f (0) .+xn n! fn (0)

f(0) x 1! f (0) + x2 2! f (0) .+(-1)^n xn n! fn (0)

f(1) + x 1! f (1) + x2 2! f (1) .+xn n! fn (1)

12 + Mcqs in Taylor Mclaurin Series 3 in Engineering Mathematics Page 1 McqOptions

1.	Find the solution of differential equation, ^dy _dx = xy + x², if y = 1 at x = 0.
A.	(1- frac{x^2}{2!}+ frac{3x^4}{4!}- frac{15x^6}{6!}+ )
B.	( frac{x}{1!}+ frac{3x^3}{4!}+ frac{15x^5}{6!}+ )
C.	( frac{x}{1!}- frac{3x^3}{4!}+ frac{15x^5}{6!}- )
D.	(1+ frac{x^2}{2!}+ frac{3x^4}{4!}+ frac{15x^6}{6!}+.. )
Answer» E.

Discussion

2.	Expand (1 + x)^{¹ _x}, gives ___________
A.	e[1 + <sup>x</sup> <sub>2</sub> + <sup>11x<sup>2</sup></sup> <sub>24</sub> - ..]
B.	e[1 <sup>x</sup> <sub>2</sub> + <sup>11x<sup>2</sup></sup> <sub>24</sub> - ..]
C.	e[<sup>x</sup> <sub>2</sub> <sup>11x<sup>2</sup></sup> <sub>24</sub> - ..]
D.	e[<sup>x</sup> <sub>2</sub> + <sup>11x<sup>2</sup></sup> <sub>24</sub> - ..]
Answer» C. e[<sup>x</sup> <sub>2</sub> <sup>11x<sup>2</sup></sup> <sub>24</sub> - ..]

Discussion

3.	Find the expansion of Sin(lSin^-1 (x)).
A.	(lx- frac{l(1-l^2)}{3!}x^3+ frac{l(1-l^2)(9-l^2)}{5!} x^5- )
B.	(lx+ frac{l(1-l^2)}{3!} x^3+ frac{l(1-l^2)(9-l^2)}{5!} x^5+ )
C.	(1-lx^2+ frac{l(1-l^2)}{3!} x^4- frac{l(1-l^2)(9-l^2)}{5!} x^6+ )
D.	(1+lx^2+ frac{l(1-l^2)}{3!} x^4+ frac{l(1-l^2)(9-l^2)}{5!} x^6+ )
Answer» C. (1-lx^2+ frac{l(1-l^2)}{3!} x^4- frac{l(1-l^2)(9-l^2)}{5!} x^6+ )

Discussion

4.	Find the expansion of cos(xsin(t)).
A.	( sum_{n=1}^ ( frac{x^n [Cos(nt)]}{n!}) )
B.	( sum_{n=0}^ ( frac{x^n [Cos(nt)]}{n!}) )
C.	( sum_{n=1}^ ( frac{x^n [Sin(nt)]}{n!}) )
D.	( sum_{n=0}^ ( frac{x^n [Sin(nt)]}{n!}) )
Answer» C. ( sum_{n=1}^ ( frac{x^n [Sin(nt)]}{n!}) )

Discussion

5.	Given f(x)= ln (cos (x)),calculate the value of ln (cos ( ₂)).
A.	-1.741
B.	1.741
C.	1.563
D.	-1.563
Answer» B. 1.741

Discussion

6.	Find the expansion of e^xSin(x)?
A.	(e^{xSin(x)}=1+x^2-x^4/3+x^6/120- )
B.	(e^{xSin(x)}=1+x^2+x^4/3+x^6/120+ )
C.	(e^{xSin(x)}=x+x^3/3+x^5/120+.. )
D.	(e^{xSin(x)}=x+x^3/3-x^5/120+ )
Answer» C. (e^{xSin(x)}=x+x^3/3+x^5/120+.. )

Discussion

7.	Find the expansion of f(x) = ln (1+e^x)?
A.	(ln(2)+x/2+x^2/8-x^4/192+ . )
B.	(ln u2061(2)+x/2+x^2/8+x^4/192+ . )
C.	(ln u2061(2)+x/2+x^3/8-x^5/192+ . )
D.	(ln u2061(2)+x/2+x^3/8+x^5/192+ . )
Answer» B. (ln u2061(2)+x/2+x^2/8+x^4/192+ . )

Discussion

8.	Expansion of y = Sin^-1(x) is?
A.	(x+ frac{x^3}{6}+ frac{3}{40} x^5+ frac{5}{112} x^7+ .. )
B.	(x- frac{x^3}{6}+ frac{3}{40} x^5- frac{5}{112} x^7+ .. )
C.	( frac{x^3}{6}- frac{3}{40} x^5+ frac{5}{112} x^7 .. )
D.	(x+ frac{x^2}{6}+ frac{3}{40} x^2+ frac{5}{112} x^2+ .. )
Answer» B. (x- frac{x^3}{6}+ frac{3}{40} x^5- frac{5}{112} x^7+ .. )

Discussion

9.	The expansion of e^Sin(x) is?
A.	1 + x + <sup>x<sup>2</sup></sup> <sub>2</sub> + <sup>x<sup>4</sup></sup> <sub>8</sub> + .
B.	1 + x + <sup>x<sup>2</sup></sup> <sub>2</sub> <sup>x<sup>4</sup></sup> <sub>8</sub> + .
C.	1 + x <sup>x<sup>2</sup></sup> <sub>2</sub> + <sup>x<sup>4</sup></sup> <sub>8</sub> + .
D.	1 + x + <sup>x<sup>3</sup></sup> <sub>6</sub> <sup>x<sup>5</sup></sup> <sub>10</sub> + .
Answer» C. 1 + x <sup>x<sup>2</sup></sup> <sub>2</sub> + <sup>x<sup>4</sup></sup> <sub>8</sub> + .

Discussion

10.	The expansion of f(a+h) is ______
A.	(f(a)+ frac{h}{1!} f'(a)+ frac{h^2}{2!} f (a) .+ frac{h^n}{n!} f^n (a) )
B.	(f(a)+ frac{h}{1!} f'(a)+ frac{h^2}{2!} f (a) . )
C.	(hf(a)+ frac{h^2}{1!} f'(a)+ frac{h^3}{2!} f (a) .+ frac{h^n}{n!} f^n (a) )
D.	(hf(a)+ frac{h^2}{1!} f'(a)+ frac{h^3}{2!} f (a) )
Answer» B. (f(a)+ frac{h}{1!} f'(a)+ frac{h^2}{2!} f (a) . )

Discussion

11.	The necessary condition for the maclaurin expansion to be true for function f(x) is __________
A.	f(x) should be continuous
B.	f(x) should be differentiable
C.	f(x) should exists at every point
D.	f(x) should be continuous and differentiable
Answer» E.

Discussion

12.	Expansion of function f(x) is?
A.	f(0) + <sup>x</sup> <sub>1!</sub> f<sup> </sup> (0) + <sup>x<sup>2</sup></sup> <sub>2!</sub> f<sup> </sup> (0) .+<sup>x<sup>n</sup></sup> <sub>n!</sub> f<sup>n</sup> (0)
B.	1 + <sup>x</sup> <sub>1!</sub> f<sup> </sup> (0) + <sup>x<sup>2</sup></sup> <sub>2!</sub> f<sup> </sup> (0) .+<sup>x<sup>n</sup></sup> <sub>n!</sub> f<sup>n</sup> (0)
C.	f(0) <sup>x</sup> <sub>1!</sub> f<sup> </sup> (0) + <sup>x<sup>2</sup></sup> <sub>2!</sub> f<sup> </sup> (0) .+(-1)^n <sup>x<sup>n</sup></sup> <sub>n!</sub> f<sup>n</sup> (0)
D.	f(1) + <sup>x</sup> <sub>1!</sub> f<sup> </sup> (1) + <sup>x<sup>2</sup></sup> <sub>2!</sub> f<sup> </sup> (1) .+<sup>x<sup>n</sup></sup> <sub>n!</sub> f<sup>n</sup> (1)
Answer» B. 1 + <sup>x</sup> <sub>1!</sub> f<sup> </sup> (0) + <sup>x<sup>2</sup></sup> <sub>2!</sub> f<sup> </sup> (0) .+<sup>x<sup>n</sup></sup> <sub>n!</sub> f<sup>n</sup> (0)

Discussion

Explore topic-wise MCQs in Engineering Mathematics.

Find the solution of differential equation, dy dx = xy + x2, if y = 1 at x = 0.

Expand (1 + x)1 x, gives ___________

Find the expansion of Sin(lSin-1 (x)).

Find the expansion of cos(xsin(t)).

Given f(x)= ln (cos (x)),calculate the value of ln (cos ( 2)).

Find the expansion of exSin(x)?

Find the expansion of f(x) = ln (1+ex)?

Expansion of y = Sin-1(x) is?

The expansion of eSin(x) is?

The expansion of f(a+h) is ______

The necessary condition for the maclaurin expansion to be true for function f(x) is __________

Expansion of function f(x) is?

Find the solution of differential equation, ^dy _dx = xy + x², if y = 1 at x = 0.

Expand (1 + x)^{¹ _x}, gives ___________

Find the expansion of Sin(lSin^-1 (x)).

Given f(x)= ln (cos (x)),calculate the value of ln (cos ( ₂)).

Find the expansion of e^xSin(x)?

Find the expansion of f(x) = ln (1+e^x)?

Expansion of y = Sin^-1(x) is?

The expansion of e^Sin(x) is?