Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

Q: 5 +1 Tsimplify denomina 7) (1+i) (1-1) = 4 the Following without using the de noctor Prove that

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Q: S ³+3 dz

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Q: (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g)…

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Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

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Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

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Q: Use the substitution u= x² + 6 to find the following indefinite integral. Check your answer by…

A: To evaluate the integral.

Q: Q4: (chose one only) 3-x 1- f(x) = 2 x 2 a) Find limx→2+ f(x), limx→2- f(x) andf(2). b) Dose limx-2…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: ΒΣ 3 Θέλη

A: 3.The given series ∑n=0∞3.12n

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j - k, find: (iii)A. (B+C)and (A + B).C (iv)…

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Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k 41 +5/-6k i (C): If w = tan x and…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x = T-3 π .

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y= 11e²x, y(0) = 1, y'(0) = 1 2x 7e -7.x +…

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Q: 2/4 + ²/81 + ²/1/729 t. Ⓒ274

A: 2.Solution:29+281+2729+.......29+292+293+.......this series is geometric series.Common…

Q: Use L'Hopital's to determine the limit. lim 0 0 1 1-cos x I O sin x COS X as x approaches 0

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Q: Q2: Find the 1. y = 1- 2. y [In(x² + 2)²]³ 3. y = xcsex tan² (cos x) 4. y for the following…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: Calculate approximations of tan(π/4-0.1) by using Taylor polynomials P₁(x), P2(x), P3(x). Use c=π/4.…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: In Problems 17-26, solve the initial value problem. dy y(0) = √3 dx y' = x³ (1-y), 1 dy 2 dx dy…

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Q: dy 5: Find for the following functions: dx (1) In (x - y) = xy + y³; (2) y = tan³ √/cot(7x); (4) y =…

A: Since we are given with multiple number of question and answered according to the guideline

Q: The radius of a right circular cone is increasing at the rate of 6cm/sec while  its altitude is…

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Q: Solve the given initial-value problem. y(x) = y" + 6y'7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 11e2x 7e…

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Q: Q2: Solve the following integral (1) 7x²+14x+15 (x²+3)(x+7) dx dx ; (2)

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1…

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Q: fe e sin xdx

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Q: (B): Find the tangent equation to the curve y = sin²x at point x =

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Q: (b) If G(x) = CV: 1 cos (t¹) dt, compute G'(x).

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Q: find the area of the triangel with verticies A=(0,0,0) B=(2,1,1) C=(3,1,2) round to 2…

A: This question can be solved using the concept of area of triangle using vectors.

Q: Q2: Solve the following f (1) 7x² +14+15 (x²+3)(x+7) dx :

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find S н - 2+ dx

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Q: Verify that the function satisfies the three hypotheses of Roll's Theorem on the given interval.…

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Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

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Q: 2 -1 -x²+8x-4 dx 1 x(x²+x-2)

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Q: A spherical raindrop evaporates at a rate proportional to its surface area with (positive) constant…

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Q: 4 (A): If A 2 2 1 Find AB and AC. 01 0; 1-2 -1 1. 2 B = 2 ܚ ܨܢ ܝ 1 ܚܕ ܨܐ ܝܕ -2 -2 and -1 2 1 C: 11…

A: Here, the given matrices are: A=420210-2-11, B=2312-2-2-121, C=31-3026-121

Q: Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2,…

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Q: SULWAY 5. x- 7. dx 9. dt In Problems 7-16, obtain the general solution to the equation. dy -y-e³x =…

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Q: 7. Use integration tables to find or evaluate the integral. (Use C for the constant of integration.)…

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Q: 2) × 2+4i 3+1 and 2=3-1 2+i 2 prove that x² + 3xy + y² = 6 if it was

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Q: Solve the given initial-value problem. y" + 6y'7y= 11e²x, y(0) = 1, y'(0) = 1

A: Given :y''+6y'-7y=11e2x

Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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Q: Find dy x 3 In (x - y) = xy + y²

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Q: If R is the region bounded by the graphs of the functions f(x) = 2 + 5 and g(x) = x + ½ interval [1,…

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Q: Given that 0. ∞ n=0 x = 1 1 <- x to x = = Identify its interval of convergence. The series is…

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Q: Q2/A Cylindrical tank with radius of (3 m) and height of (10 m) has initially filled with water. In…

A: Please see the below picture for detailed solution.

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Evaluate the integral and check your answer by differentiating. x8 + 8x5 x7 1 dx +C

A: Firstly expand the fraction of given Integral and then integrate

Q: Solve the initial value problem y" + 4y + 4y = 0, y(-1) = 5, y'(−1) = 6. y(t) = =

A: The given initial value problem is y''+4y'+4y=0,  y(-1)=5, y'(-1)=6

Q: Use substitution to evaluate the definite integral given below. 1² (Enter an exact answer.) Provide…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j - 6k du

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