43. Let f(x) be a continuous function. Express (2) + (2) + + lim as a definite integral. +(A)

Q: Consider the following initial value problem, defined for t > 0: dy dt a. Find the Laplace transform…

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Q: Which graph represents the reciprocal of y=(x+2)²-3? A B La C D U home

A: The function is  y=(x+2)2-3

Q: x = 5 tan 8 8= 0

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Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. ∞ (2) Σ…

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Q: 1 The vector field F = is conservative. Find a potential function for F compute SF dr, where C is…

A: To find the given line integral.

Q: Given f'(x) = 3x4 - 4x³ + 7. Determine which interval the graph of f is concave upward. (a.) x > 0…

A: To determine the interval where the graph of f is concave upward

Q: What form of the particular solution is appropriate for the differential equationy"- y'=4? (A) y =…

A: Solution: Given differential equation is, y"-y'=4

Q: Suppose F = (5x - 5y)i + (x + 5y)j. Use Stokes' Theorem to make the following circulation…

A: We need to solve using Stokes' theorem.

Q: Given f(x) = ax³ + bx² + 9x + c. Find a so that (2,3) is a point of inflection of the graph of f and…

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Q: What is the general solution to the the differential equationy""' = 0? A y=C₁+C₁₂x+C₂x²+C₁x³…

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Q: f(x, y) = e 10x-z²+8y-y² Find and classify all critical points of the function. If there are more…

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Q: 3. Decide if the given sequence {a} converges, or diverges. If it converges, determine the limit of…

A: If the limit of the sequence at infinity is finite then sequence is convergent.  If the limit of the…

Q: If f(x, y, z) = 6 √2x+8y +9z, then fz at x = 0, y = 0, z = 1 is =_ 00 -3 01 09

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Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: We have to find the area using geometry.

Q: Find the area of the region enclosed by y=6x and y=5x2

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Q: Find the surface area of the part of the sphere x² + y² + z² = 9 that lies above the cone 2 = √x² +…

A: To find the surface area of the part of sphere lying above the cone.

Q: If the supply and demand functions for a commodity are given by 6p -q = 60 and (p + 2)q = 4830…

A: given  6p-q=60.......1           (p+2)q=4830........2from equation  1,   q=6p-60  put in euqation 2

Q: Find the points on the cone z² = x² + y2 that are closest to the point (4, 2, 0). (x, y, z) (smaller…

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Q: 2. Building X is 100ft tall. Building Y is 200ft away from building X, where the distance is…

A: We can solve the given problem by using the trigonometric formulas.

Q: Evaluate the indefinite integral. Use C for the constant of integration. S sin (+) √ 1 + cos(+) d+

A: Find the indefinite integral

Q: 29. [(5x-7)-² dx = k(5x-7)¹ + [√x+1dx=k(x + 1)/² + C (4-x)-¹ dx = k ln 14-x|+C 30. 31.

A: Given problems:- 29.  ∫5x-7-2dx=k5x-7-1+C 31.  ∫4-x-1dx=kln4-x+c

Q: Use identities to find values of the sine and cosine functions for the angle measure. 8, given that…

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Q: Calculate the integral approximation Se for S6 = 8. 1₁4² dz.

A: Given:    ∫-104-x2dx Simpson's rule S6:   ∫abf(X)dx=∆x3fx0+4fx1+2fx2+... where ∆x=b-an,       a=-1,…

Q: . (2,3), (4,-5)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: d. f(x) = (2x-3)5 (2x²- e²x)-3

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

Q: Evaluate SS √1 + x² + y² dS where S' is the helicoid: r(u, v) = u cos(v)i + u sin(v)j + vk, with 0…

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Q: 2. [xc xcos 3xdx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the least squares app (-2, 0), (-1, y(x) =

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Q: area of the region enclosed between f(x) = x² + 2x + 11 and g(x) = 2x² + x − 1.

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Q: Evaluate the following integrals analytically: Cπ/2 #1 #2 #3 (8 + 4 cos x) dx 3 [² (1 - e²^x) dx [²₂…

A: The given integrals, 1. ∫0π28+4 cosxdx 2. ∫031-e-xdx 3. ∫-241-x-4x3+2x5dx We have to solve these…

Q: 1. Fill in the table below. (x, y) (-3,0) (4,3) (0,5) (r, 0) 5, π

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Q: Sketch the graph of y = x³ - 6x² + 9x + 1 by first finding the following a) the intervals on which y…

A: Given :   find first derivative  equate to zero to find critical point

Q: blem 3. : Use the Comparison Test to determine w 1 Σ In(n) n=2

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Q: If m≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: 4. Use the table in the book to find the Taylor series for the function, centered at the specified c…

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Q: Create a Cartesian graph and then a polar graph for each: a) r=3+2sin theta

A: need to graph the Cartesian equation and then polar equation

Q: Given f(x) = ax³ + bx² + 9x + c. Find b so that (2,3) is a point of inflection of the graph of f and…

A: The inflection point of the graph of f is (2, 3). So,                  f''(x)=0 at (2, 3)⇒6ax+2b=0…

Q: Find the points of intersection of the two graphs y = sin (2x) and y = 2 cos²(x) for 0 ≤ x < 2.…

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Q: Question 9 Which of the following is the complete set of roots of the auxiliary equation…

A: We need to choose correct option.

Q: onvert the line determined by the symmetric equations - 2 y+1 - 3 form. -2 parametric t) = t) = t) =…

A: Given query is to find the parametric form of the line.

Q: Consider the following demand function with a constant slope. Let Q(p) describe the quantity…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Use properties of a right triangle, trigonometry, and implicit differentiation to determine the…

A: By using the properties of a right triangle, trignometry, and implicit differentiation to determine…

Q: Consider the function in the graph to the right. The function has a relative maximum of 3 o at x = 0…

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Q: Find the Laplace transform F(s) = L{f(t)} of the function f(t) = 8th(t - 2), defined on the interval…

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Q: Find dy/dx. x= t/7+t, y= sqrt(7+t)

A: Given Equations:- x=t7+t y=7+t

Q: x² 3 (x³ – 9)³ This can be transformed into a basic integral by letting Consider the indefinite…

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Q: The profit function for a certain commodity is P(x)=120x-x²-1100. Find the level of production that…

A: GivenThe profit function for a certain commodity is P(x)=120x-x2-1100   We need to findThe level of…

Q: 1. If the region to be rotated is bounded by two curves, and the typical rectangle extends between…

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Q: Consider the line y = ax, where a is a positive constant. What should be the x-coordinate of the…

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Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. ∞ (b)…

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