√72² +4 7x6 + 4x + 2√x dx

Q: Evaluate the integral using the indicated trigonometric substitution. S dx, 6x³ √x²+36 X = 6 tan(0)

A: The integral is ∫6x3x2+36dx   ; x=6 tanθ

Q: A mountain climber is about to haul up a 40-m length of hanging rope. How much work will it take if…

A:

Q: Please describe the answers step by step since it is difficult to figure it out since the answers…

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Q: 9. The marginal revenue function for the company is given by 0.000045x² -0.03x +3.75 0≤x≤500 Recover…

A:

Q: Let g(x) = 5x²-3. (a) Find the average rate of change from -4 to 5. (b) Find an equation of the…

A: Here we have a function g(x) need to find the average rate of change and equation of the secant.

Q: Find the vector that has the same direction as (6, 3, -2) but has length 2.

A: Given: Vector 6,3,-2 We are required to find: Vector of length 2 in the direction of given vector.

Q: After substitution is performed, which of the following is equivalent to S² x√√4x²+9 dx?

A: To calculate ∫02x4x2+9dx.

Q: Sketch the region R whose area is given by the iterated integral. 16 *16 - X [²[* y 8 6* [* d 16 14-…

A: To sketch the region R whose area is given by the iterated integral: ∫08∫0x dy dx + ∫816∫016-x dy dx…

Q: 10T (12 + x) Find the first few coefficients. Co = 0 C1= Suppose that C2 C3 C || Immentari C4 = 10…

A: .

Q: 1. Determine the intersection (if any) of the following planes. Show your work clearly and be sure…

A: (a).The given planes are:π1:  2x+y-3z=5π2:  3x+4y+3z=6

Q: 1. The series meets the conditions to use the ratio test, and lim 11 00 A. M8 an converges n=1 B.…

A:

Q: Evaluate the integral. 3 19-x² √9-x² 19-x²-2² -√9-x²-2² 1 (x² + y² + z²)1/2 dy dz dx =

A:

Q: Suppose seafood price and quantity data for the years 2000 and 2009 follow. Use 2000 as the base…

A: We need to find relative price and weighted price.

Q: Find the angle 8 between the vectors in radians and in degrees. 5 [cos(3)i + sin(37)] 4 (²7)₁] u = 5…

A:

Q: The graph of f is shown below. (Click on a graph to enlarge it.) Evaluate the following integrals by…

A:

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

A:

Q: The equation y= 2e65 is a particular solution to which of the following differential equations? B D…

A: An equation,

Q: Find the area between the curves. 12 11 y=x y = 10x 1 1 11 The area between the curves is (Type an…

A:

Q: Graph the line passing through the given point and having the indicated slope. through (1,1) with…

A: Given a point (x1,y1) and slope m. Need to find the line and graph it.

Q: Consider the following initial-value problem. f'(x) f'(x) dx = = 2 VX f(x) = I Integrate the…

A:

Q: Differentiate each of the following: y = e^Inx

A: given y=elnxformula used→(i) d dx(xn)=nxn-1(ii)  we know→ elna=a

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A:

Q: ing the graph shown a. Find g(1) b. Solve g(x) = 1 C. Find g(1) d. Solve g(x) = 1 -2 -1 g(x) 2 1 -1…

A: Here given that a graph of g(x) and x and we find value of g(1) and other.

Q: Find the exact area between the graphs of y = x^3 + 7 and y = -x + 7 for 0

A: Area under the curve y1 and y2 is given by A = ∫( y2 - y1 )dx

Q: Use the law of sines, the law of cosines, or the Pythagorean Theorem to solve AABC. A = 96%, B =…

A:

Q: A three-sided fence is to be built next to a straight section of river, which forms the fourth side…

A: Area of rectangular region, A = 1800 m2.

Q: 2 2. Evaluate: [x(x² − 1)² dx 1

A:

Q: 34 x-²-2 y=-l y x= X

A:

Q: Eliminate the parameter (NO SPACES). - x = 2t - 3 and y = 9 – 4t y =

A: given→⇒x=2t-3............(1)⇒y=9-4t.............(2)

Q: Find the equilibrium point. 1) D(x) = (x-7)2, S(x) = x² + 2x + 1

A:

Q: Evaluate the following integral by interpreting it in terms of areas from drawing the graph of the…

A: Given data

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A:

Q: Construct a function that passes through the origin with a constant slope of 1, with removable…

A: This type of discontinuity can be removed just by defining f as that limₓ→ₐ = f(a) Here we have…

Q: Use the Limit Comparison Test to determine if the following series converges or diverges. 00 Hint:…

A: The given series is: ∑n=1∞n-3n3+8n2+6

Q: find maximum and minimum of m(t)= 0.00291^3t + 0.00904t^2 -0.16t +122.81

A: mt=0.00291t3+0.00904t2-0.16t+122.81 Find the maximum and the minimum value of the given function.

Q: - Determine the given indefinite integral f(2x+1)x²x²+2x dx

A: let  B=∫(2x+1)e2x2+2xdxB=∫(2x+1)e2(x2+x)dxwe know→(i)  d dx(xn)=nxn-1(ii)  ∫eaxdx=eaxa+c

Q: Let f(x) = √x + 6. Calculate the difference quotient f(10+h)-f(10) h h = .1 h = .01 - h=-.01 h -.1…

A: Let fx=x+6

Q: Find the equation of the tangent line to f(x) = x² at x = 1. 4 3 2 1 (a) y= -1 -1 -2 -3 -4- 1 a

A: e

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A:

Q: III. 2. Consider the function x<0 0SAS1 (1) At what points is this function continues? (2) For each…

A: fx=1+x2, x&lt;0ex2,      0≤x≤11+x2, x&gt;1

Q: d d Calculate[ri(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

A: We need to perform differentiation.

Q: Pollution levels in a lake have been modeled by the equation x = 0.03 + 0.18e−0.35t where x is the…

A: The given equation x=0.03+0.18e-0.35t, where x is the volume of the pollutants and t is the time in…

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. 15 8' x in Quadrant II sin(2x) tan(x)…

A: To find out the trigonometric functions shown in the question.

Q: Determine if the series converges or diverges. Give a reason for your answer. Σ n=1 2n 9n-4

A: By divergence test if the limit value finite then the given series is diverges

Q: Consider the function f(x) = - In this problem you will calculate Rn Show hint The summation inside…

A: The given function is:f(x)=-x23+4

Q: For the following polynomial function f(x)= x³ + 4x²-2, state if the Intermediate Value Theorem…

A:

Q: Evaluate the indefinite integral /(cos(2x) - V +VIR √x +3¹ + + sec²(x)) dx.

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Q: Use the Integral Test to determine whether the series is convergent or divergent. Σ Evaluate the…

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Q: Find the total area of the shaded regions. Ay 3- 2- 0- -1- 5 C... Q Q The total area of the shaded…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is and the given…

Q: For the parametric equations: 10e 10t (write the number answer only in the box) (i) (dat at t=0 dy…

A: