k! (ii) ek k=1

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A: Given integral is ∫x2-x2-1 dx.

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A: To determine whether the given statement is true or false.

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Q: ху x+

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Q: (Ca' - x*

A: we know that,           integration of xn dx = xn+1n+1.  and x-y2= x2+y2-2xy

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Q: r³ – 4x – 1 = 0 3 | Consider the implicit curve throughout this problem. Find dy/dx and use this to…

A: We can solve as follows

Q: (2x + 4) + 1 dx- x² + 4x + 5 x² + 2x– 10 2 (2x + 4) + 1 2 Consider dx = x2 (x² + 4x + 5) dx.…

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Q: Find the function f(x) such that f''(x) = x + cos(x), f(0) = 1, and f'(0) = 2.

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Q: dx x2 — 2х — 4

A: I=∫dxx2-2x-4=∫dxx2-2x+1-5=∫dx(x-1)2-52

Q: x +6 (a) Find dx. (1– 2x)(x² +3)

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Q: 2 - V2r + 10 a. lim 1-3 r2 + x – 6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

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Q: 15x2 — х3 — 43х - 19 The integral J (x + 1)²(x² – 6x + 13) can be rewritten as Ах + B C D + + bx + c…

A: Given problem:-

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Q: Consider . x2 +2x- 10 2 2 (2x + 4) +1 dx evaluate dx = x² (x² + 4x + 5) (2x+4) +1 dx - x² + 4x +5 -…

A: Topic = Integration

Q: Find the saddle point/s of the function f(x,y) = x + y² +x²y+4 O a. (E ,-1) & (- 2 -1) O b.(4,0) &…

A: Let's find.

Q: 3. CHOOSE ONE. Assume that r0. 5x (a) Transform the Cartesian equation = 5x – 5xy into a polar…

A: A)5x2x2+2y2=5x-5xy12x2+2y2=1-yx=r cosθ, y=r sinθx2+y2=r212r2=1-1(rsinθ)r sinθ=1-12r22r2-1=2r3…

Q: Using Integration By Parts. x3 x2 +4 dx =uv- v- Svau- -Svdu. Find uv- 3 글x리 (x2 + 4)Z-/글x(x2+ 4)2 dx…

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Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

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Q: 1 Using Integration By Parts, x sec x tan 2 1 -uv-Jvau Find u v- Svdu '2x sec 을x-J25ec을x dx o 1 2*…

A: From the given problem; ∫xsec12xtan12xdx=uv-∫vdu    ....1   We know that; ∫secxtanxdx=secx+C

Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: A doll-manufacturing company wishes to create a display box with a square base and open front side.…

A: Let's find.

Q: 3. A water tank has the shape of an inverted circular cone with base radius 4 m and height 8 m. If…

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Q: Find all points (x,y) on the graph of y = x-4 with tangent lines perpendicular to the line y = 4x +…

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Q: BLUsing the following table, find f(x) as polynomial in x: -1 3 6. F(x) -6 39 822 Good Lup 3.

A: Let's find.

Q: 2 (х + 2y)dx + (у - х)dy %3D 0

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Q: dx Using Trigonometric Substitution find f(0) 3 (x² + x + 1) 2 4 3 sec? e O 3 sec? e 4 O 3 sec e 4 3…

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Q: /9– x² using Trigonometric Substitution what is dx ? onsider x2 3 sec e de P 3 cos e de O 3 sec e…

A: Topic:- application of integration

Q: Given the equation below, find dy/dx* 6x^3+2x^30 y+y^4= 9 dy/dx= Now, find the equation of the…

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Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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Q: A stone is dropped from the upper observation deck of a tower, 800 m above the ground. (Assume g =…

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