2 - V2r + 10 a. lim 1-3 r2 +x – 6

Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

Q: Determine whether Rolle's Theorem can be applied to f on the dosed interval [a, b]. (Select all that…

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Q: -Svau Using Integration By Parts, x Arcsec 3x dx = uv- - Svau- Find uv- x² Arcsec 3x dx V9x2 – 1 o 1…

A: Here we have to solve the integration by using integration by parts.

Q: evaluate intel9a) Evaluate intelga

A: Use property of integral.

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x? + xy + y? - 9x…

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Q: In each of the problems, solve the given differential equation. 3. xy` = (1 - y2)1/2

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Q: 2x+11 3 1 dx . evaluate Consider 3 dx = x2 + x- 6 1 dx : x+3 - X- 2 x+3 x- 2 X-2 In |x+3 +C x+3 In…

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Q: Evalute the indefinite integral

A: To evaluate the integral.

Q: 9. The graph of f(x) = x* + 8x3 – 72x2 + 6 is concave down for A. -6 2 С. х< -6 D. -3 – 3/5 <…

A: The function id concave downward if f''(x)&lt;0

Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y? - 8x + 16…

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Q: X+ 6 2) lim х-6 (х-6)2

A: limx→6 x+6(x-6)2=6+6(6-6)2=120

Q: ind the points of inflection of the graph of the function. (Order your answers from smallest to…

A: Here, the given function is: f(x)=x(x-4)3 So,…

Q: Using Integration By Parts, Vx In 2x dx =uv- -Svdu Jv du Find UV- du O 2 늘 xVX In 2x-| Vx dx Xx In…

A: A detailed solution is given below

Q: Decide whether the limit exists. If it exists, find its value. fx) 3+ 2+ -2 -1 3 X -1+ -2- 1) lim…

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Q: Find the area between the curve and the x-axis over the indicated interval. 7 y =; [1, 6] ... The…

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Q: Suppose i = (-3, –3, –5) and v = (-1, –5, –1). Then ů x ở is and i x ũ is

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Q: Vx2 + 4x - 5 dx = Using Trigonometric Substitution f(e)dA find the new limits of integration. 1. x+2…

A: Let's find.

Q: Find dy/dx by implicit differentiation. xe - 18x + 4y = 0 %3D dy %3D xp

A: Given:   To determine: dy/dx using implicit differentiation.

Q: 100 10) y = 2 + 9e-3x

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Q: the substitution formula to evaluate the integral. 4 cos³ x sin x dx T/3 27) 15 A) 15 B). 15 3276 D)…

A: Given query is to find the value of the integral.

Q: Using Integration By Parts, x3 V x² +4 dx = u v- -[vdu Find UV-

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Q: Eveleate inter ssin(2x) dx

A: We can find the integration as below.

Q: Using Integration By Parts, x3 / x² + 4 dx = u v - v- Svau-

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Q: Find the indefinite integral. (Use C for the constant of integration.) sinh(5 – 2x) dx

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Q: Suppose a sample of a certain substance decayed to 77.2% of its original amount after 300 days.…

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Q: Solve the equation. Write the solution set with the exact values given in terms of common or natural…

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Q: Using Integration By Parts, Vx In 2x dx = u v - v du Find u v- ſv du O 3 xVX In 2x-|응Vx dx 2 xVx In…

A: We can solve this as follows:

Q: 18) From a thin piece of cardboard 40 in. by 40 in., square corners are cut out so that the sides…

A: let "x" be the height of square corners which are cut outso, Box has length =40-2x, width =40-2x ,…

Q: C. ta the sum or the values of a and h such that f(x) - 2ax2 1 hr + 3 has a relative extremum at the…

A: 7.   The function f(x)=2ax2+bx+3 has a relative extremum at the point -1,2

Q: * tan°(x) cos“(x) 1 tan7(x) 1 tan (x) O tan7(x),

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Q: dx Using Trigonometric Substitution J- 3 sin e+C express the answer in terms of x. (x² + x + 1) 2 4x…

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Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x6…

A: For critical numbers, Put g'(x) = 0 and solve for x.

Q: Given that A = (1,0,2) and B = (6, -2,3), solve for projąB.

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Q: Rewrite the expansions in terms of exponential and simplify the results as much as you can. cosh 5x…

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Q: Evaluate the integral. In 2 tanh x dx

A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

Q: Solve the equation. Simplify your answer if possible. y-4 y y+9 +1 The solution set is

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Q: | cot2 x dx 1 ot x + C cot x - х + с cot x + x + с О -cot x —x+C

A: Given query is to find the the integral.

Q: Sketch the curve y = x* - 6x? and show intercepts, maxima and minima and points of inflection.

A: Follow the procedure given below.

Q: *(5t² – 3t=3) dt

A:

Q: In7 Change the Cartesian integral dx dy into an equivalent polar integral. Then evaluate the polar…

A: Put x=rcosthetha and y=rsinthetha

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: Suppose that P dollars in principal is invested for t years at the given interest rates with…

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Q: 1. Cosxdx Rubrics: Integration process Antiderivative Substitution of limits Computed/Analysis of…

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Q: x2 +x+1 dx. Use partial fractions 2x2 +2+x³+x

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Q: Find the average value of f over the given rectangle. f(x, y) = 2x2y, R has vertices (-5, 0), (-5,…

A: Let's find.

Q: Evaluate the line integral, where Cis the given curve. (x + 6y) dx + x² dy y (6, 1) C (7, 0)

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