-S₁ Consider 08 14/3 O 17/8 05 3x5 3x4+6x³-3x²-6x •√(x-1 -dx- Using the method of partial fractions, the given integral can be written as + 1² + 1. x-m+ B x+1 + с x+m Jde-F dx- Find the sum of A. B. and C.

Q: 5. (4xdy + 3ydx) + x³y² (xdy + ydx) = 0 Ans: 6x³y² + x6y6 = c

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Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Topic:- application of integration

Q: Given the vector function r(t) = (+1, 1-2t², 8t-4), find the are length of this curve on the…

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Q: 4. Express the following limit of the Riemann sum n lim (x + x² cos x; ) Ax, n→∞ i=1 ㅠ where x₁ =…

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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: Evaluate tan" (x) secx dx. 1 A n(m + 1)(x). m+1 1 (В -tan (m + 2)(x) + m+2 1 -tan (m+1)(x). m+1 1…

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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: for the implicit equation zey +In(y) = x³-12? da dy 3x2 02-2 = xey + Y 3x² - ey dy da xey + What is…

A: Topic = Derivative

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: Given that f xdx = 1/2 and f²dx = compute the integral [*(1-x)²dx.

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Q: Enter a whole or decimal number, or DNE for does not exist or undefined. |0x| lim (5+10=¹). [ - -0+z

A: Topic = Limits

Q: 5. Evaluate the following triple integral. ſſſ (.x² + y² ) dx dy dz D D={(x,y):x² + y² ≤9.15:53)

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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: (c) y = 1, y = 1/2, x = 2 (d) y = √x, y = 22, x=9 (e) x = 2y², x = 4 + y² (f) x = 1 - y², x = y² – 1…

A: The area between any two curves is given by formula A = ∫ [f(x) - g(x)] dx  with limits from a to b…

Q: Evaluate Stan" (x) sec¹x dx 1 A m+1 I m+3 B 1 -tan (m + 1)(x) +- m-1 1 -tan (m + 3)(x) + m+1 -tan…

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Q: Use the slopes of tangents to determine whether the function -6x2+36x is increasing, decreasing, is…

A: Given function, f(x)=-6x2+36x We know that function is said to be increasing when f'(x)>0, and…

Q: Find the equation of the tangent line to the curve y = 5x² - 7 at a point x = 1.

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Q: Evaluation. 1. Determine the antiderivative for each. Show complete solution. √ 5x³=3 dx 2. √(√x√x +…

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Q: d the equation of the tangent line to the graph at the specified value of x. y=x√3-x², z = 1.

A: Given query is to find the equation of the tangent.

Q: ➡pose m and n are constants and m ‡n. Evaluate sin(mx) cos(nx) dx` 1 -cos(m-n)x- -cos(m+n)x] + C n-m…

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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: To evaluate x²cosx dx' use integration by parts. What is the expression after the second integration…

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Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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Q: Find 3√√²+9 3 rdr Option 1 2√2-27 (√27-3) Option 2 (2√2-27)

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: The objective is to find the slope and equation of tangent line.

Q: Evaluate 3 TIT 4xyzdxydydz O 15 O 15/2 10 о None of the choices

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Q: 5. Determine vector and parametric equations of the plane that... a) has the scalar equation 2x-y+…

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Q: dx The integral ·S= can be transformed to which of the following when trigonometric substitution is…

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Q: To evaluate [x²cosx dx' -2 / COST. 2sinx -2/cosx 2 / COST x2sinx – 2x cost x2sinx+2x cosx − 2 x2sinx…

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Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

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Q: need the answer quickl

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Q: Suppose m and n are constants and m #n- Evaluate * sin(mx) cos(nx) dx cos(m+n)x] + C 1 −cos(m−n)x+·…

A: Indefinite Integration

Q: Let f(x)=2-3√. Then the expression can be written in the form where A, B, and C are constants.…

A: Solved below.

Q: S = Consider O 14/3 O 17/6 O 5 0 6 3x5 3x4+6x³3x2 - 6x A B C • √(₁-1² + + + + ² S x-1 x+1 x+m d.…

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Q: Calculus Effect of Luxury Tax on Consumption Government economists of a developing country…

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Q: To evaluate A B [x²cc x²cosx dx use integration by parts. What is the expression after the second…

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Q: 43. Evaluate: (2ex - 4x) dx A. 2ex - 4x + C B. -2ex + 4x + C 4x C. 2ex + C In 4 4x D. 2e + + C In 4

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: Find the area bounded by the trigonometric curves O2.828 square units 1.414 square units 3.667…

A: topic - area bounded by curves

Q: Let f: CD be a function, with C being the domain and D being the codomain. Show that for any C₁, C2…

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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: QUESTION 6 ·S. sece tane de sece - 1 The integral cose de 1-sine sec²0 de 1+tano sine de 1+ cose x…

A: Let's transform given integral.

Q: Given the following pieces of information: I. a = (4, -2, 3) II. b = (0, 3, -5) Find: a) lal b) ab…

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: 3x5 3x4+6x³3x² - 6x B с + + x + 1 x+m Consider S А Sx √x-m+A x-m+ 14/3 17/6 6 5 -dx. Using the…

A: solution

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: eading due north at 500 km/h. If it encounters a wind from the northeast at 1 sultant velocity…

A: We will solve the problem.

Q: dx ·S= can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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Q: Question Find the area A of the region that is bounded between the curve f(x) = ex-2-3 and the line…

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Q: Find the derivative of the function. 4 24 y=. VF X X

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Given problem:- Use double integral polar coordinates to find the area of the portion of the surface…