·S- For x 1/2 dx and using the substitution=x1/2, the resulting integral takes t U -du 1-u² 4u 4-4² 4u S- U -du (2u2) 2 -du -u4 -du

Q: Q4: Convert the following polar integral to Cartesian Integral in order (1) dx dy (2) dy dx T 6 csc0…

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Q: 4. Evaluate the following triple integral. [ƒÃƒ‚²‚x² sin y dy dz dx .

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Q: Question 1. Let f(x,y) = y²e¹x. (a) Find the linearization L(x, y) of the function f at the point…

A: To find the linearization.

Q: (B) 1 1 −tan (m+3)(x) + _—__——_—_tan (m + 1)(x) + C · m+3 m+1

A: Let us use trigonometric substitution. After solving we get correct answer is option-(B) as shown in…

Q: In this problem, you are asked to carefully read Example 6.4.2 of APEX Calculus. 1 The given…

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Q: If f(x) = 24x + 12, find the slope of the secant line between the values of x₁ = - 1 and ₂ = = 2.

A: Topic = Function

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: Suppose m and n are constants and m #n. Evaluate I sin O 1 1 -cos(m-n)x- - cos(m+n)x+ C n-m m+n 1 1…

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Q: Provide all answers to four (4) decimal places. Applying the Gauss-Seidel method in solving the…

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Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

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Q: 3. Evaluate the following integral by using the polar coordinates. £²₁, [x²=²²* (x² + y²)³¹ dy dx.

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Q: What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx-B) + C?

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Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin² z, Z = [0, π]

A: Given.   x^2+y^2=sin^2z

Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: Given

Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) c) is…

A: Concept: The equation of the line segment parallel to the given axis and passing through the point…

Q: a. Find the first derivative. f'(x) = b. List any critical values. c. Identify intervals of…

A: As per the guidelines we can solve 3 parts only

Q: 2 I зах 9x²-6x+5

A: On solving this we will get

Q: 2 Find all local extreme values of f(x) = + 2x² + 6x + 80. - 3 The FIRST local extreme value, moving…

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Q: Evaluate tan tan" (x) sec¹x dx O 1 −tan (™+2)(x) + — tan” (x) + C m+2 m O 1 1 -tan (m + 1)(x) — — ¹…

A: To evaluate the integral

Q: S- x² + seco tan de sece - 1 sec²0 de 1+tano sine de 1 + cose cose dᎾ 1 - sino The integral [se S I…

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Q: Text Canada's population is about 33 million people. It is increasing at about 1.8% per year. How…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: 2. Differentiate the following: a. y = 2x-2y b. 2sinxcosy=1

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Q: x² - 25 to fill in the table: Xx - 5 6 5.5 5.1 5.01 Based on ONLY the table of values above, what…

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Q: When applying the u-substitution technique to this integral, we will need to exchange dx for du. 99…

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Q: 25. Which of the following value of x is continuous of the function f(x)=√4x²? A. 2 C. 4 B. 3 D. 5

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Q: dx (x²+4)² The integral A÷/csc²³ Ⓒ + /sec²0 B C Ⓒ + / sin² D 8 csc ³0 de c³0 de cos²0 de sin ²0 de…

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Q: Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: ve [No.5] -2 2 зах 9x²-6x+5

A: On solving this we will get

Q: Given the function f(x) = = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x)…

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Q: Estimate the slope of the tangent line to the curve at the given point (-3.5,1.250) on the graph to…

A: In this question, we want to find the slope of the tangent line of the curve at point (-3.5, 1.250).

Q: Evaluate S tan" (x) sec¹x dx. I A tan (+1)(x)tan (-1)(x) + C m+l - 1 I B tan (+3)(x) +tan (+1)(x) +…

A: Let's evaluate given integral.

Q: 16. Evaluate the integral or show that it is divergent dx x+1 1 (a) √ (3x+1)³², I (3+1), (b) /…

A: We need to find out here  integrals.

Q: Let u = 1-16x². For the integral with respect to u, one limit of integration will be 1. What is the…

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Q: Fill in the Blank 1. u is

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Q: Evaluate the integral S√x Inx dx 3 2 4 -x² Inx+ x² + C 03x³nx-x²+c 4 2 -x² Inx+ 2 C 15 3 2 4 °²x²nx…

A: We have to solve above integral

Q: ·S S For S- x 1/2 -dx and using the substitution=x 1/2, the resulting integral takes the form: 4u…

A: topic - indefinite integral

Q: 2. A cheetah chase a deer which is 100 m ahead. The time in which the deer takes 10 leaps the…

A: We have to use simple logic to solve the problem

Q: x1/2 S dx and using the substitution = x 1/2, the resulting integral takes the form: x-x³ U A / du U…

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Q: QUESTION 7 ·S sin²t sin²0 de csc³0 de sec ³0 de cos²0 de The integral dx (x²+4)² 01 Secto 0 + can be…

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Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx-B) + C?

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Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

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Q: Consider two athletes running at variable speeds v₁ (t) and v₂ (t). The runners start and finish a…

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Q: lim F(x) lim F(x) x--6 What is the value of the limit? Select the correct choice below and fill in…

A: We have to find the limit

Q: The rose r = 3 cos (50) is shown below: 3 -3 Find the area of the region bounded by one loop of the…

A: We need to find area.

Q: Evaluation. Determine the antiderivative for each. Show complete solution 1. S dx 5x³-3 √x3 2.…

A: As we know that; The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1       1).…

Q: 3 Question 5 Example 6.4.2 of APEX Calculus uses this fact (which appears in an integral table): f…

A: The objective is to find the right option.

Q: Exercises To Solve [No.5] 4 S (X-+1) √ X ²2X-3 3-2x-x²

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Q: 48. Evaluate: A. (x + 1)³/² + C 5 B. (x + 1) 5/3 + C C. (x + 1) 5/² + C D. (x + 1) 5/4 + C 49.…

A: As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And The common integral; ∫eax+bdx=1aeax+b+C…

Q: What is the value of f(1) - 16B in ∫x^3 lnx dx= f(x) ( (1/4) lnx - B ) + C

A: To find out the required value.