Find the indefinite integral. Check your result by differentiating. 10x dx Step 1 Observe that is the derivative of (6 + x²). Let g(x) = (6 + x*). Multiply and divide the integrand by | and rewrite the integral. 10x 10 dx = (6 + x²)³ xp (x)_(x + •) /-

Q: Use the chart below to find the average rate of change of the function f(x) over the interval given.…

A: Our Aim is to find the average rate of change of the function f(x) over the interval given.

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Q: Find each function value and limit. Use -∞ or co where appropriate. 7x* - 14x2 f(x) = 8x° +4 (A) f(-…

A: topic- functions and limits

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Solve the following

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Q: Identify the End Behaviors for the function graphed to the right 5+ Right hand end behavior: 3 As x…

A: Given query is to find the end behaviour of the function.

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Q: Solve 12 sin (t) + 2 cos(t)- 8 = 0 for all solutions 0 <t < 277 t = Give your answers accurate to 2…

A: The given equation,      12sin2t+2cost-8=0

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Q: Unless specified, all approximating rectangles are assumed to have the same width. The graph of the…

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Q: Write the sum 5 + 15 + 45+ + 1215 using sigma notation. ... a1(1 – r") - Then evaluate the sum using…

A: Solve the following

Q: 00 Determine whether the series omverges absolutely, conditionally, or n=1 not at all.

A: The given series is ∑n=1∞-1n-1nn2+1. A series ∑n=1∞un   is absolutely convergent if ∑nun  is…

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: b). Using gamma function, evaluate Sx6 e-2x dx

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Q: Use the graph of the function f shown to the right to estimate the indicated function values and…

A: topic- limits

Q: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

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Q: Find the limit 1-ex lim x+0 10x2 – 18x

A: Here we have to use the concept of limit.

Q: 4. Find the volume of revolution generated by revolving the region between f(x) = 9-3x and f(x) =…

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Q: Find an equation for the plane through the points (3, 4, 33), (2,1 -2), (0, 1, –1). The plane is

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Q: Find the volume of the solid of revolution when the region bounded by y = x + 1, the x – axis, and…

A: Recall: Shell method,  V=2π∫abr(x)h(x)dx We have, a=0, b=2, r(x)=3-x, h(x)=x+1

Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: Ift=2cos (y² + 2), find the derivative of t with respect to y. A. 8y sin(y² + 2) cos(y² + 2) B. –8y…

A: The given function,  t=2cos2y2+2

Q: Find the point at which the line meets the plane. x = - 3 + 5t, y = 3+ 6t, z = - 2 + 3t; x + y +z =…

A: Given ; Line meets plane = ?   x = -3 + 5t   y = 3 + 6t   z = -2 + 3t   Plane;        x + y + z =…

Q: Find dy/dx of 6x² – 4y² = 10 at (1, 2) 3/2 None of these 4/3 -3/4 4/3 On the circle x + y? = r²,…

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Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

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Q: 3

A: We will find the limit.

Q: Write an equation for a rational function with: Vertical asymptotes at x = -1 and x = 1 x intercepts…

A: Solve the following

Q: 20. Find f2x/(5x-3)dx

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Q: Refer to the figure below to find the limit lim f(x). X - 00 3.5- 2.5- 1.5- 1- 0.5- 2.

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A: We can find the limit of the function. Firstly make factor in numerator and denominator and solve .…

Q: Evaluate the given limit |. lim %3 1- x2 2. lim CosX

A: 1. limx→0+1x-1ex-12. limx→∞x1cosx

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Q: the

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Q: #3) Rewrite the integral 27 .2 p dr d0 0. in rectangular coordinates.

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Q: Suppose $15000 is invested at 7% interest compounded continuously. How long will it take for the…

A: Suppose $15000 is invested at 7% interest compounded continuously. How long will it take for the…

Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

A: sum of number is 23 let a number = x  other number is 23 - x

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

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

Q: 13. The distance s, in metres, fallen by a skydiver t seconds after jumping (and 160(:1 – 1 + e-5.…

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Q: Let R be the region of the 1st quadrant enclosed by x=y^2 , x=2-y^2 ,y=0 . 1.1 Draw an area R.…

A: Given that;  x = y^2   and x = 2 - y^2       Let's find area between two curve in 1st quadrant.

Q: dy without first solving for y. dx e implicit differentiation to find ² + 3x + xy = 100 the given…

A: Topic:-  application of derivatives

Q: For an arithmetic sequence, a17 = 2. If the common difference is 5, find: aj = the sum of the first…

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Q: dy as a function of x. dx Write the following function in the form y = f(u) and u = g(x). Then find…

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

Q: For each function, determine the long run behavior x2 + 1 has Select an answer x2 + 2 x3 + 1 has…

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Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduce to…

A: To find the mass.

Q: Find the indicated derivative and simplify. 2x - 4 y' for y = 2 + 8x %3D

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Q: Find the number(s) b such that the average value of f(x) = 6x? 42x + 70 on the interval (0, 6 is…

A: The average value of f(x) in the interval a,b is given by, 1(b-a)∫abf(x)dx

Q: 1. Determine the exact value(s) of k for which the planes x– 2y + kz + 7= 0 and x– 2y – 2 = 0 have…

A: Note: According to our answering guidelines we have to answer only one question if multiple…

Q: 8/16/22, 140 PM The Sine & Cosine Laws State whether the given measurements determine zero, one, or…

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