Show that lim(x+¹)=e².

Q: Evaluate: ¹xe¹dx O -∞ O None of these 00

A: We have to find the integral.

Q: Find the derivative off when f(x) e-2 4-x 4 1. f'(x) = 2. f'(x) = 3. f'(x) = 4. f'(x) 5. f'(x) = = 5…

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Q: A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the…

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Q: The kinetic energy of an object with mass m and velocity v is given by: k= If a ball weighing 2kg is…

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Q: Sketch the region enclosed by the given curves. y O -5 -10 y = 7 cos(x), y = 7-7 cos(x), 0≤x≤ # 0.5…

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Q: Let f(x): f'(x) = and f"(x) = = 7x² 4 - 3x -. Then

A: Given query is to find indicated derivative.

Q: पी T [-3, 3] Graph of f b The graph of the function fabove consists of four semicircles.if g (2) = /…

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Q: Solve the following differential equation. Show your complete solution. ( x + y -6)dx + (x - y +4)…

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Q: Suppose that f(x) = −9x¹/6. Evaluate each of the following: f'(2) = -0.8418 f'(5) = -0.4724

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Q: Find the value of f'(4) when f(x) = -³/2 +2x¹/2. 1. f'(4) = 5 2. f'(4) = 4 3. f'(4) = 6 4. f'(4) =…

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Q: The accompanying graph shows the position of a bicyclist after t hours. Assume s is positive when…

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Q: Let u (0,5, 2) and = (2, 5, -3). (a) Find u - v: v-19 (b) Find the magnitude of the vectors & and 7:…

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Q: (x + y)dx + 2x - y dy = 0 (2x-35) 465) 2x - y dy = (x + y)dx -3) dy

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Q: Suppose that f is a differentiable function such that f(1) = 5 and ƒ'(1) = 3. Use the product rule…

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Q: Use the graph to investigate the following limits. (For each limit, enter an integer. If an answer…

A: limx→af(x) exist if limx→a-f(x) =limx→a+f(x)

Q: Find Əf ax and Əf Əy 2 f(x,y) = √2x² + y²

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Q: Find the particular solution for this differential equation given the condition where y(1) = 1.

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Q: ^+) - J = = ^p(4 – () тар(L-Ата)

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Q: True or false: True False d dx 2 + ² = 1/2 2+ - X

A: d(xn)dx=nxn-1d dx(constant)=0f(x)=2+1x

Q: Write the following difference as a single logarithm. Assume all variables are positive. log5 (4)…

A: log54-log513

Q: Let Evaluate the following specific values of f': (A) ƒ'(1) = (B) f'(4) = f(x) = 8x¹/3(x³ - 4).

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x³ 3x - y3 +12y + 9, D is…

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Q: 19. The solution to (2x - 4y - 3)dy =(x-2y)dx is: c. a. 6y-x² - 4xy + 4y² = c b. 6y + x² - 4xy-4y² =…

A: To solve the given differential equation

Q: Find the curvature of the curve r(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t = 0 Give your…

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Q: Find the points on the curve given below, where the tangent is horizontal. (Round the answers to…

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Q: 8 Let f(x) = 6 +. X (a) Find ƒ'(x). ƒ'(x) = 8 x² - (b) Find the slope of the tangent line at x = 2.…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Suppose f(t) = 6 t² (a) Using the definition of the derivative, calculate the derivative of f. (F…

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Q: 22. sin x 2 dx -11 + x²

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Q: 7 Calculate the second and the third derivative of y = 4x - E -14 3 x 3": y"=1

A: y=4x-7xy=4x-7x-1d dx(xn)=nxn-1d dx(constant)=0

Q: An object thrown vertically upward from the surface of a celestial body at a velocity of 49 m/s…

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Q: A linear function is given. g(x) = 2x - 16 (a) Sketch the graph. No Solution…

A: we have to make graph using above equation

Q: The substitution best used in: da +x+³x is

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Q: Find the extreme values of f on the region described by the inequality. (If an answer does not…

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Q: Find the left hand and right hand derivative of the function.  f(x) =absolute value of x^3  at the…

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Q: If a projectile is fired with an initial velocity of vo meters per second at an angle a above the…

A: Given that x=(v0cos(α))t   and y=(v0sin(α))t-12gt2 , g=9.8m/s2

Q: Let f(x) = 5+7x². If h ‡ 0, then the difference quotient can be simplified as f(x+h)-f(x) h = Ah +…

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Q: Fill in each box below with an integer or a reduced fraction. (a) log₂ 83 can be written in the form…

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Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers. x² - 2x…

A: Please see the below picture for detailed solution.

Q: Determine F'(r) when F(x) = -2rf'(x) + f(x) and f is a twice-differentiable function. 1. F'(x) = -3…

A: F(x)=-2xf'(x)+f(x)d dx(a.b)=a×dbdx+b×dadx

Q: The position of an object at time t is given by the parametric Sx = 2t² + 4t equations Y 2t² + 7 =…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: Evaluate the integral. (Use C for the constant of integration.) [cos-¹(x) dx

A: let G=∫cos-1dx∫udv=uv-∫vduddx(cos-1x)=-11-x2∫xndx=xn+1n+1+c

Q: 12. For what function M(x,y) will the differential equation M(x,y)+(x²+x)dy=0 be exact? a. 2xy-y b…

A: To find the function for which the differential equation is exact

Q: Solve the following differential equation. Show your complete solution y' = x-4xy

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Q: Find T and N for the space curve, where t> 0. r(t) = (9 cos t + 9t sin t)i + (9 sin t - 9t cos t)j +…

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Q: Find the linear function with the following properties. f(-6)=-4 f(-4)=6

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Q: The length of arc s of a curve from x = a to x = b is given by the formula s = fest a 1+ dy dx 3/2…

A: Given: y=0.14x32      from x=0 to x=200 To find the length of the cable

Q: Find the limit 13 a) lim x-3 X+3 2 x 9 c) lim X->0 3-) 2 b) lim (6x² - 6 cos x) = 17² ? X->0 2 5 COS…

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Q: What is the particular solution x³ - 2xy; when x = 1, y = 1? a. y=x² +e(¹-x²)_1 D. 2y=x² +2e(1-x²) —…

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