In 8 thy ể dxdy.... ****** Ans: 2 e. *******

Q: dx √1 + 4x²

A: Let's evaluate given integral by using trigonometric substitution.

Q: Question 4. Continuity Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x =…

A: We have to show f has removable discontinuity at x=3 and find the value of c

Q: a) 4x²y - 3xy³ + 6x; d) e²x+3y; b) xy; e) x+y x-y c) xy²; f) 3x²y-7x√y.

A:

Q: Solve the initial value problem. y" - 9y" - 400y = 0, y(0) = y'(0) = y(0) = 0, y"(0) = 246

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find curl F if F(x,y,z) = 7exy i-8 cosy j +5 sin²z k. curl F = -7xexy k curl F = -7xexy i curl F =…

A: In this question, we want to find the curl of given vector function.

Q: wal u a Write the vector shown below as a combination of vectors and 7 shown above. a Vector - 21+ V…

A:

Q: 7. Given a = (0, 1, 3), b = (4, 5, 6), then a · b = a. 1 b. 24 8. Given a = (0, 1, 3), b = (4, 5,…

A: Let's solve. Two vector a and B are given.

Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions, labeling…

A:

Q: Given that f(x) = (x - 2)² and g(x) = 1 - 3x, find (a) (f + g)(4)= (b) (f - g)(4)= (c) (fg)(4)= (d)…

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Q: Question 2 Find two numbers whose sum is "a", if the product of one by the cube of the other is to…

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Q: Select the correct answer to the following problems: a) f(x) f(x) dx ○ f(4) 00 ○ f(0) f(x-4) f(x)dr…

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Q: Find the value of b for which the differential equation (yelory + x) dx + (bxe¹0ry) dy = 0 10xy is…

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Q: П 2 0 KIN 2 p² sinr de dr dø 0

A:

Q: 6dx X – - 3√/x²

A: Given

Q: Find the Volume: Rotate the region bounded by y = √x, y = 3 and the y-axis about the y-axis

A:

Q: 2 dydx -23-1 (xy)³ SS.

A:

Q: 22 Determine if lim(x,y)→(0,0) x²y² 2X4+Y4 exist

A:

Q: Solve the integral shown below. So cos¹¹ 3xdx Só 11

A: ∫0π6cos113xdxLet u=3x.=∫0π2cos11u13du=13·∫0π2cos11udu=13·∫0π21-sin2u5cosuduLet…

Q: -0.2 e2x sin(x) dx

A:

Q: Question 5. Limits at Infinity; Horizontal Asymptotes For the function f whose graph is given below,…

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Q: The curves 7₁(t) = (– 2t, t³, tº) and 7₂(t) = (sin( – 2t), sin( – 4t), t – π) intersect at the…

A: Here, the given curves are: r→1(t)=-2t,t5,t6 and r2→(t)=sin(-2t),sin(-4t),t-π which intersect at the…

Q: 8 Determine the area of the region bounded by the curves y = =, y = 2x and x = 4

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Q: Let 7' (t) = Find a parametric equation of the line tangent to r(t) at the point (59, 0, - 2.303)…

A: Follow the procedure given below.

Q: Evaluate using Partial Fraction Decomposition: (- 2. -dx

A: Use partial fraction to evaluate the integral

Q: f(x csc² 2x - x cos x cos 2x)dx

A:

Q: Find the coordinates of the vertices of the polygon after the indicated translation to a new…

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Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: 5- The tail of vectors a and b form two sides of a parallelogram. Vectors is 30 degrees, and the…

A: Area of a parallelogram when two sides of the parallelogram are given by the vector a→ and b→ is…

Q: (a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC-area…

A: Let's solve for area of the triangle.

Q: Find the Volume: Rotate the region bounded by x = y²-6y + 10 and x = 5 about the y-axis

A: A detailed solution is given below.

Q: Evaluate sec(log x) -dx x In | sec(log x) + tan(log x) | +C 1 log e In | sec(log x) + tan(log x) |…

A:

Q: A rectangular field is to be fenced off along a river where no fence is needed on the side along the…

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Q: dx 4-9x²

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Q: Using the Maclaurin series expansion of e, to find the series expansion of f(x). Express [ f(t) dt…

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Q: Q1 (a) Interchange the order and evaluate the integration a+c 2x fa* ft* xy² dydx 0 a-2 c-6

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Q: A coulomb is the same as; * O Ampere.second Ο Ο Ο Ο Ampere.second^2 Ampere/second Ampere/second^2

A:

Q: dx √3 1 + x²

A: we use the  formula ∫dx1+x2 = tan-1 x    +C

Q: During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s…

A: According to the company policy we are supposed to answer only first three sub parts and rest of the…

Q: 4dx 3 x - √√x² S

A: We will use simple Integration rules to solve this question.

Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: Which of the following is equal to In 4 ? 4 offen O et dt 1 O ln 3 + ln 1 dt of - In 8 In 2 t

A:

Q: II. Solve the initial value problems given the following: dy 2 if y(-1) = 21. = -2x + 3x dx dy -2x…

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Q: √√3 L dx 1+x²

A:

Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

A:

Q: limg0 (csc y Arcsing”

A: Given problem:- limy→0cscyArcsiny2

Q: 5 ;ㅣ

A: We have to find first four terms of give series.

Q: (c) S x+4 x²+5x-6 2 dx

A:

Q: Use the power series expansion of ƒ(x) = 1 x)²· 1- x for x < 1 to find a power series ex

A: Remember power series expansion for f(x)=11-x; x&lt;1 is  f(x)=11-x=∑k=0∞xk

Q: Question 8 Evaluate: lim-1 (3-22)tan (7). e 3m 01 O None of the choices O e

A:

Q: Q3) Determine the maximum point of the function f(x) = x(5-x) with Fibonacci search method, if the…

A: Here, we have fx=x5π-x. The number of experiments to be performed are n=4 and the first uncertainty…