Evaluate the definite integral. i+e"j+t k)dt 15t (el3 – 1) i – (e~1 – 1) j +k i- (e - 1) j+, k O els – 1 15 O el5 – 1 - (e" - 1) + 15 O els – 1 i+ (e- – 1) j+; k 15 O els i- ei+k

Q: How many real valued solutions over (-1,1) to the following ODE?

A: given odinary differential equation  y'=x1-y'+ylnlny'+eπxy claim-  to check how many solution does…

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Q: y=Sin x -37 30 Ly= cos x - 37 -2 77 ST 377 2. HN - 15

A: Answer is mentioned below

Q: If e/2i -/2i = sin2 then z = - 2i In(sin2) – 4kn 2i In(sin2)+ 4kT - 2i In(sin2) + 4kTt

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Q: 2 x = (y-1)² x = 3 y 1 X = 2√y 2 x

A: Step 1:Step 2: Step 3: Step 4: thanks

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Q: 04.2 If x=7i-j+k, y = 3í - j - 5k and z = 9i + j - 3k Show that xx (y+z) = (x x y) + (x x z)

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Q: Use Green's Theorem to evaluate -15/4 O -218/3 O 19/2 [(6y - 9x) dy - (yx - x³) da where C' is shown…

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Q: Solve the First ODE (3y* – x*)dx = 3xy'dy || 4-4ln(2x)+c А-у %3D 4 4-4ln(x)+c B- y = 2 4-4ln(x)+c C-…

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Q: A Moving to another question will save this response. Question 10 "The product of a negative real…

A: Let us assume a negative real number x. So, x<0 And a positive real number y. So, y>0

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Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: 49

A: ln4te6t

Q: Performing iterations on (25) respectively, leads to the following: n-1 X2km+j v; II n-1 Y2km+j…

A: Given: 2km+j=2km+j2+rj To find: Corresponding equation

Q: Example 3. Let fr (1) =12k+1, ke No. (3.10) Then Dft =R and system (2.49) becomes 2k+1 + 'n-2 (ax +…

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Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

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Q: |2x+1 2x 1 f(x)= |2x 5 g(x)= 3 functions how much ? 2x 3 1- O A) 256 O B) 64 O C) 32 OD) 16 OE) 128

A: f(x) = 3(2x+1) -5(2x)         = 3(2x.2) -5(2x) = 2x  g(x) = 3(2x) -2x = 2(2x) = 2x+1

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Q: t is the direction of fastest increase at (-3, 4, -4) for the function f(x, y, z) = 1 x² + y² + z²

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Q: 2. 16X (x-6)(X+2) x +B

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Q: 1. (а) 52x $* (b) 3' x 32 - 5 2. (a) k* x k? (b) m³ x m 3. (а) у к (-у") (b) -x (-)

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A: Use improper integral

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A: We have to solve the given ordinary differential equation.

Q: Find y " if y = 2x sin x. O A) y" = - 4 cos x + 2x sin x O B) y " = 2 cos x - 4x sin x C) y " = - 2x…

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