Find the equation of the tangent line to the graph of the given equation at the specified point. y = (5x2 – 6)-3; x = -1 y =

Q: Evaluate the integral mx sin nx dx

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Q: Evaluate the integral sin3 x + cos? x + 1 dx J sin² x (cos² x + 1)

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Q: What is the equation of the given ellipse? YA

A: Vertex ( -3 , 2 ) covertex ( -1 , -1.5 )   Center= ( h , k )= ( -3 , - 1.5 )   Major axis b = 2 - (…

Q: x + 4 dx x² + 2x + 5

A: ∫x+4x2+2x+5dxx+1 is a scalable factor of x2+2x+5, so divide x+4 by x+1=∫x+1x2+2x+5dx+∫3x2+2x+5dx

Q: Find y' if y= 2x + Vx*-9xr+3.

A: We can find y' in the following steps.

Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = x2 - 7x + 6 g(x) -x2 + 5x + 6 y 10…

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Q: Find the integral of your answer in problems 2a and 2b.

A: We can solve this as follows:

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x - c² and y = c – a is 60…

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Q: Find the area under the curve y=sin2x from x=0 to x=3pi/4 A. 2 B. 1/2 C. pi D. 3/2…

A: The curve y=sin2x from x=0 to x=3π4

Q: 12sin3xcos7x dx

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Q: Solve for fxx, fxy, fyx and fyy given f(x, y) = 2 ln(x − y).

A: The given function is:fx,y=2 lnx-y.We need find fxx, fxy, fyx and fyy

Q: e-(x²+y³)(x dx + y dy) = 0

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Q: Given f(x) = r³ – 2x2 – x + 2 on [1,2]. Verify the three conditions of the hypothesis of Rolle's…

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Q: 3. A rectangle is inscribed under the curve of f(x) = e-*², where one side of the rectangle lies on…

A: Follow the procedure given below.

Q: Calculate

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Q: 5. Determine the values of x for which the function is continuous. x + 5 x² – 5x + 4 3x +1 2x2 – 8x…

A: a. fx=x+5x2-5x+4b. fx=x4-x2c. fx=3x+12x2-8x Note:     Multiple parts are given, we are answer only…

Q: dy/dx - y = xy5 = 0 Ans. 1/y* = -x++ ce 4*

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Q: sec 3xtan3x dx

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Q: Evaluate the integral (Trigonometric Substitution) x*dx J (x² + 4)² 2

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Q: 3. COSX + sin x +1 dx 2 cos?x (sin?x+1)

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Q: y-axis Consider the graph shown to the right 4. lim f(x) X-axis 5. Evaluate lim f(x) X-3 6. lim f(x)…

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Q: Two transverse waves y1 = 2 sin(2nt - x) and y2 = 2 sin(2rt - Ix + T/2) are moving in the same…

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Q: 2. [Growth of a tumor] When the radius of a spherical tumor is 6 mm, it is growing at a rate of 0.1…

A: To determine how fast the volume is changing.

Q: 2. Write the given (total) area as an integral. (vde a. The area above the x- axis and below y = 4–…

A: Here we have to find the area.

Q: 12sin3xcos7x dx

A:

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: Find: d/dt (1/square root of 2t) A. square root of 2t/4t B. - 1/square root of 2t C. 1/2t square…

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Q: 27. In how many ways can each of the following be drawn from a standard deck of 52 cards? three…

A: As per guidelines we can solve only first three sub part of the question. Solution From a standard…

Q: Let v=5i+2j. Find a vector that is twice the length and points in the opposite direction as v.

A: This is a problem related to vector. Based on the general formula and concept we will answer the…

Q: Assume the acceleration of the object is a(t) = -9.8 meters per second. (Neglect air resistance.)…

A: Given data÷ As you have suggested i have solved all steps of part 1.

Q: 5. A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his…

A:

Q: sin' xcos³x dx 3

A: Given: I=∫sin7xcos3xdx   As we know that; The trigonometric identity; sin2x+cos2x=1 The Power rule:…

Q: A problem or equation of the tangent line to a curve at the point (1,3) is y = x+2. If at any point…

A: Let's find.

Q: 4e-1dx = 7.96 × 10° O True O False

A:

Q: Find the centroid of the region bounded by y = Vx, y = 0, and x = 9. This region is covered by a…

A: We have to find the coordinates of the centroid.

Q: The multiple choice answers to choose from are A) (lnx)^2 B)2x^(lnx-1) lnx C) x^lnx-1 lnx D) 2lnx/x

A: We can simplify the answer: 2xlnxlnxx=2·xlnxx·lnx=2·xlnx-1·lnx  Because xaxb=xa-b=2xlnx-1lnx

Q: 4. The temperature, T, in "C, of a side of beef t hours after it is put in the freezer is given by…

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Q: Describe the graph of the equation. r = 19 sin 2t i + 19 cos 2t j O It is a circle of radius 19 in…

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Q: Evaluate the integral (Partial Fraction Decomposition) xdx (x² + 2)(x² + 1)2

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Q: (2х — 8)dx 2 — 6х + 18

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Q: 2. Solve for x the equation sin1 3x - cos1 2x = 6

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Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact…

A: Work

Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

A:

Q: Consider the following series. 8 + e-n n = 1 What does the Test for Divergence reveal about this…

A: We know the necessary condition for the convergence of a series. A series ∑nan   is convergent…

Q: 4. The temperature, T, in "C, of a side of beef t hours after it is put in the freezer is given by…

A: Given

Q: Evaluate the integral (2х — 8)dx х2 — 6х + 18

A: We know that integration power rule is - Integration of xn is xn+1/n+1+ C  Here C is integration…

Q: Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: dy +…

A: Use Euler method

Q: Find the area of the largest rectangle with one corner at the origin, the opposite corner in the 1st…

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Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

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

A: