3. Determine which of the fol 2" (a) n=1 n! (d 1 (b) (e n=1 2n 3n n+1 (c) (E 3n n=1

Q: (D2 + 5D + 4)y = 3-2x, Find Yp O a. 11 O b. 00 8 | O d. 11 8 X 11 X 8 3 OC. 11 X + 3 8 3 O e. none X…

A: SOME TERMS ARE EXPANDED BY USING BINOMIAL EXPANSION WHICH IS AS FOLLOWS-:…

Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

A:

Q: What is the value of Σ n=1 (A) 15 8 (B) O A B C D E (-3)^²+1 5" 9 8 - ? (C) colc (D) / (E) 15

A:

Q: (3x²-1) 5x3-5x+13 - dx equals In 15x³5x + 13| + c In 15x³ - 5x + c 5 O 1 In 15x³ - 5x + 13| + c 5 In…

A:

Q: of 2 + [y] 8+ {2 ²³ = 12; n 3+2=13°54 and {n} + y + 2-472 y + [2] = 14.7 then find

A: Given: x + [y] + {z} = 12 [x] + {y} + z = 13.54 {x} + y + [z] = 14.7 We need to calculate the value…

Q: 2. Evaluate: S 0 trư √2 = x + x dx

A:

Q: 2. (a) If z = 1+ 3i and v = −2 − i then 1 A. + 2 B. Tin Tin + C. A. 2√6 e-in/6 B. 2√3 e-in/3 D. 2 10…

A:

Q: 2. Evaluate 3 dx -) S (x+5)(2-3)dx, (b), (c)²-22²-da, J ■) x³ −2x² −4 −1+ int: (c) 1 + ² + ²/1/2 x³…

A: Topic:- application of integration

Q: n п(3п — 1) E(3i – 2) = (for n > 1). i=1 2.

A:

Q: How did you get "This is equal to (1/2) iff x = N - 1, x - 1 = N - 2, ....... , x - (n - 2) = N - (n…

A:

Q: Which of the following is TRUE? 2x2+1is n(x2) since Cx222x²+1 for all x 21 where C=3. OA. n is a (n3…

A:

Q: 2n [3] (b) E for n 21 2k k=0

A: Answer

Q: (D3-2D2-5D +6)y=e4x, Find Yp O a. 1 24 Ob. 1.4% O c. 1 4x 4x O d. 1 4x e 18 O e. none

A:

Q: d 1 ds [(s + b)n_ + b)n L(t²e¹⁰t) = (−1)n+1. Find n - b.

A:

Q: Find the value of c if ∞ (1 + c)−n   n = 2 = 1

A:

Q: (2) Assume X(@) 0 for all o e Q then which of the following is not true: (a)4-r X+X ±1 (b) XX = 0…

A: The must be option c

Q: 25 25y" + 20y + 4y = 0

A: we have to solve the given differential equation.

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: s (x² + 1) dx O (1/3)x³ + c 2x O (1/3) x° + x+ c none of the above

A: The value of the integration ∫(x2+1)dx  is x33+x+c ,where c is constant. Therefore the answer is…

Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: 1. Find a power series for each of the following, centered at a = 0 for parts (a) (d) and centered…

A: (a) Given data: The given expression is 4/(1+2x). The expression for the power series of the given…

Q: ut. (b) 710 - 76 72 (c) m*n (e) m m2 ÷ m* (f) -25A

A:

Q: (a) e2tsin (wt +t/6)

A:

Q: You may use a table of Laplace transforms in order to answer the following questions. a) Find L[5]…

A:

Q: Suppose m> n. Show that L x"

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Q: Prove the Identity H8= A(++÷)(1+ 4) %3D 2.

A:

Q: n Ralston's Method, agis equal to

A: Ralston's method  is second-order method with two stages and has a  minimum local error bound.

Q: L{ (1-t) 2}= %D 2 1 | .a S s2 S 1 2 | s2 s3 .b S4 1 1 2 .cO - s2 S3 1 2 s² 3.dO

A:

Q: 12. (I피 + |z- 2)) da – 2|) -1

A: Given: ∫-14x+x-2dx

Q: E10 (-1)(n-1) ماتلاب :find n=1 (n+1)2 Zn=D1

A:

Q: S (e3 In = + e3) dx = A. 3 + +C B. + 3e3z + C C. + 3e* +C С. 4 D. + +C 4 e3z E. 주 + + C 3

A:

Q: How many nonnegative solutions are there to the equation x1 + x2 + x3 + X4 + x5 = 21.

A: We need to find the number of nonnegative solutions of the equation  x1+x2+x3+x4+x5=21 Here, n=21…

Q: -2 -1 1 2 p(x) 1/3 k 2k 2k 1/6 : E(x) О з0/7 О 7/30 О 7/30

A:

Q: x+4 7. S (x-1)(x+3) dx = a. In|x – 1| +-In|x + 3| + C 4 4 b. In|x – 1| -In|x + 3| + C 4

A:

Q: Find L[e-6t + 7] 7 O +? 1 s2+6 S 1 7. s+6 1 7 s-6 1 +7 s-6 +

A:

Q: L{(6t + 1)µ(t-1)} e 5(65 + 1) s² S a. b. C. d. 6e e 5² S + e¯5(75+6) 5² S e $(75-6) 5²

A:

Q: ¸1(1 + r)n−¹ − 1. (n-1-1₁ r Sn (1+r)"So - P[- =

A: Sn = 1+rnS0 - P1+rn-1-1rAim: To find expression for 'n'.…