Evaluate the integral by first modifying the form of the integrand and then making an appropriate substitution, if needed. [ [ln(e*r) + ln(e−8²)] dx = +C

Q: f'(x) = (x+3)(12 - 1)(x - 14) Then the first relative extremum (from the left) for f(z) occurs at z…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: If you were to use a substitution of u = 4x³ - 2 to evaluate the definite integral below, what would…

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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: 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: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: To find derivative.

Q: The following function is positive and negative on the given interval. f(x) = 8 - 2x²; [0,4] a.…

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Q: Describe the domain and range of the function. F(x, y) = 5x² - y Domain: 0 {(x, y); x = 0} 0 ○ {(x,…

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Q: Given that 2 ≤ f(x) ≤ 4 for 4 ≤ x ≤ 5, estimate the value of 5 0³/ [ f(x)dx 5 [²₁ <5 f(x)dx

A: Given 2≤f(x)≤44≤x≤5To find range of∫45f(x)dx

Q: Determine the slant asymptote of the rational function f(x) - Oy=5x-9 Oy = 5x + 9 Oy=5x-1 Oy= 5x + 1…

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

A: I have stated the used formulas in the solution.

Q: If y₁ and y2 are linearly independent solutions of ty" + 4y' + te³y = 0 and if W(y₁, y2)(1) = 4,…

A: Need to find out the Wy1,y24

Q: Find the distance between the pair of points (5.5,7.2) and (-0.5,4.2). If necessary, express the…

A: I am attaching image so that you understand each and every step.

Q: Skill Building In Problems 13-24, use the graph on the right of the function f. 13. Is fincreasing…

A: Please see the answers below.

Q: Use the method of reduction of order to find a second solution of the differential equation t²y"…

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Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

Q: A polynomial function g(x) has a negative leading coefficient. Certain values of g(x) are given in…

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Q: Q5: Find for the following functions: dx (4) y = x sinh 2x-cosh 2x (3) y = e* sin² x In√x

A: See this solution in below

Q: Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be…

A: Solution is given below:

Q: 3. 2 洲 dx

A:

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: Compute u v if u and v are unit vectors and the angle between them is

A: topic- dot product of vectors

Q: The following table shows the daily receipts in millions of dollars of the movie "Avatar" for…

A: Consider the points 19,0.633,21,0.335,23,0.12,25,0.064 and 27,0.044. Find the Average rate of change…

Q: Find the general solution of the following differential equation. y" - 4y + 7y=0 NOTE: Use c₁ and c₂…

A: Given y''-4y'+7y=0

Q: aluate the following integral in spherical coordinates. This integral calculates the volume of the…

A: See this solution in below

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

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Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y² ;

A: Find the derivative

Q: -2 S² g(x) dx -6 if g(x) is an even function.

A: We need to evaluate integral.

Q: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0

A: To solve the differential equation.

Q: 2 -1 -x²+8x-4 dx 1 x(x²+x-2)

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Q: Σ(1-1) η n +1

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Q: Let f(x) = 6x√√x + f'(x) = -∞0 8

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Q: A cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4…

A: Basic product rule of differentiation is used.

Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: dw (C): If w = tanx and x = 4t³ + t ; Find dt dy

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Q: x² - 4 (a) lim x2 (x + 2)(x-3)²

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

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) S sin x+cos x sin³ x cos³ x…

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Q: 12. (2xy³ + 1) dx + (3x²y²-y¹) dy = 0

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Q: The answer above is NOT correct. Find the area of the region enclosed between y = 4 sin(x) and y = 3…

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Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

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

Q: Let g(x) = = f(1) dt, where f is the function whose graph is shown below. At what value of x does…

A: Given: gx = ∫0xftdt Using Leibniz integral rule, we get g'x = ddxxfx -  ddx0f0 g'x = fx

Q: 1. (1) E (14) (1) Choose the correct option (Multiple Choice Questions): Which of the following is a…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: At least one of the answers above is NOT correct. The velocity function is v(t) -t² + 4t - 3 for a…

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Q: 1) - 7x²+14x+15 (x²+3)(x+7) dx

A:

Q: 10. dy dx = X y²√1 + x

A:

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: We have to find out equation of tangent

Q: y = sin(x), y = 0, x=0, x= π Exercise (a) the volume of the solid formed by revolving the region…

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Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: Evaluate the indefinite integral f7 sin v cos vdv =

A: Given ∫7sin6v cosv dvTo evaluate the integral:

Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy