Instruction: Solve the following indefinite integrals. Show complete solutions.

Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bo...

A: Note: Since you have asked part b, we will solve only part b. 

Q: X+ 4x + 3

A: Given query is to eveluate the integral.

Q: Determine all the partial derivatives of f(x,y, z) = y² In(x + 2y) – In(3z) (x³ + y? – 4z) Determine...

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Q: cos x dx Vsinx

A: Topic = Integration

Q: Answer the question below: x+y The student should find the local linear approximation of f(x, y, z) ...

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Q: (y+ /x²ty? )dx- X dy = 0

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Q: 47 - tan 3. (That dot between the two trigonometric functions represents multiplicatic () Find the e...

A: Given that sin7π6.tan4π3Solution:sin7π6.tan4π3sinπ+π6.tanπ+π3-sinπ6.tanπ3        sinπ+θ=-sinθ ,tanπ+...

Q: Write an equation of an ellipse with center at (3,2), focus at (5,2), and vertex at (8,2). (x- 3)2 ,...

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Q: For the next three questions, consider the differential equation: y" – 2y' + y = e* arctan r

A: Particular Integral

Q: Given an infinite series, discuss a strategy for deciding what convergence test to use

A: First i have written an infinite series and told about convergence test of similar series named p-te...

Q: (a) Find (g/f)( x) and (fog)(x) for the functions f(x) = x2+ x and g(x) = - 2x+3. 1 a) g/f: fog: (b)...

A: Given f(x) = x2+xg(x) = -2x+3we know that fg(x) = f(x)g(x)and f∘gx = f(g(x))

Q: What are the coordinates of the foci in the equation - 4 *5=1? A F1(1,0); F2(-1,0) B F1(3,0); F2(-3,...

A: The given equation is: x25+y24=1                               (1) Equation (1) is compared with the...

Q: Determine the standard equation of the ellipse that satisfies the given properties: 16 3, horizontal...

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Q: Find the average value of f (x, y) = 4x cos(wy) over the rectangle R = {(x, y) | 0 < x < T, 0 <y < 2...

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Q: 1. Find the value of the directional derivative at the particular point Po for the given function in...

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Q: For the next four questions, consider the differential equation y" – y = x²e* +5

A: Let's find. 

Q: Let us try to find where a function is increasing or decreasing given the  following.  1. f(x) = x3−...

A: To find the function is increasing or decreasing in the given interval.

Q: Evaluate the limit lim, 5 a. 2 b. 0 C -1 x d. I

A: Given: limx→5 x+11x-1

Q: What is the derivative of (3x^2tanh(sin4x))

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Q: solve the differential equation   x(4ydx+2xdy)+y3(3ydx+5xdy)=0

A: Given that the differential equation is    x(4ydy+2xdy)+y3(3ydx+5xdy) = 0 

Q: Determine the arc length L of the curve defined by the equation y = In(6x) over the interval 1 < x <...

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Q: r(t) = ln(13 – t) i+ v9+tj- 3e¯t k t) = (

A: Given query is to find the derivative of the vector.

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: Evaluate lim -2x csc (-5x).

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Q: f(x) = 5. (a). Use f'(x) = lim (e+h)-/@) to find f'(x). %3D %3D T+3 h→0 (b). Find an equation of the...

A: Given query is to find the derivative using definition and the equation of tangent at x =2.

Q: Find the critical point(s) of the function. S(x, y) = 4e²-}+4y

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Q: det a det C

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Q: Use the given graph of the function to find the z-values for which f is not differentiable. 1.A Answ...

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Q: у (2ху+1) dz +a (1+2ху— г3 у?) dy 3 0 (1+ 2гу— а* у) dy %3D0

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Q: Problem 1. Draw a direction field for the given differential equation. By hand, sketch an approxi- m...

A: Solutionn is here

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to...

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Q: Name the quadrant in which the angle 0 lies if cot t > 0 and sint < 0. O II OIV O Not possible to de...

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Q: A trough is 3 m long, 5 m wide, and 4 m deep. The vertical cross-section of the trough parallel to a...

A: Base on the general formula of the work we will calculate the total work required for pumping fluid ...

Q: solve the differential equation: y2dx+(x2-xy-y2)dy = 0

A: Given:    y2dx+x2-xy-y2dy=0

Q: MULTIPLE CHOICE) Which of the following statement (s) is(are) true? I. y = e-/2 is a particular solu...

A:  Given perticular solution y=e^(-x/2)  And y=e^(2x)cos3x

Q: You go to the doctor and he gives you 17 milligrams of radioactive dye. After 20 minutes, 6.5 millig...

A: Given query is to find the atime taken to reah the radioactive to 2 mg.

Q: 10. Using the method of undetermined coefficients, write the form of the assumed particular solution...

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Q: The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the ...

A: The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the ...

Q: Since 3 (k + 1)³/3k+1 (1+ ±)* 1 lim k→+∞ lim k→+∞ 3 3 the series (converges/diverges/inconclusive) b...

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Q: Determine whether the series converges, and if so find its sum If the series diverges, indicate that...

A: The given series is summation of 1/(81k2+63k-8).

Q: Give linearly independent functions that are annihilated by: D5 (D- 2) (D + 3) D2(D2 – 2D + 10)

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Q: e) 1 Σ Vn n=1 3 f) 5 3 п-1 п 8 W

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Q: R has degree 4 and zeros 3 − 5i and 3, with 3 a zero of multiplicity 2.

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Q: da (cos ( 3x) sin( 2æ)) dæ

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Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bo...

A: Given: A dingly is pulled toward a dack by a rope from the bow through a ring on the deck 8 it above...

Q: O f)= e* +2x² +6xt7 -3+2y = 4x" Solue the

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Q: Answer the question below: The student should find the local linear approximation of a function in t...

A: Let's find. 

Q: 2. Use the Intermediate Value Theorem to show thatf has a zero between a and b: f(x) =x+2 x*- 6 x'+2...

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Q: 1. Given that r(t) = t²i+tj + 2k. Sketch the curve with the given vector equation. Indicate with an ...

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Q: 3. Evaluate: e-x²+2x dx (Hint: let t = (x – 1)²) %3|

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