Find the slope of the tangent line to the parametric curve 3 cos (t) (y = 2 sin(t) X = at the point F6

Q: Find the derivative of the given function. f(x) = e6 sin(x) 6 sin(x) cos(x) f'(x)= 6e What is the…

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Q: Solve the following integration :- S [ 5 Cos x dx

A: we need to find the integration.

Q: 3. Use the given number of partitions to calculate the Right Endpoint Riemann Sum, and sketch the…

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Q: A company determines that its marginal revenue per day is given by R'(t), where R(t) is the total…

A: We have to find total profit

Q: Prove that if g has an extremum value at x = c then f must have a tangent line parallel to the line…

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Q: Use Newton's method to approximate a root of the equation 327 +4x + 4 =0 as follows. Let x₁ = 3 be…

A: given equation we need to find the second and third approximation.

Q: 6. (a) The curve y = x², 0≤ x ≤ 1, is rotated about the y-axis. Find the area of the resulting…

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Q: f(x) = = x²-7x-8 x-4 For each entry, enter a single number. First Number: The smallest x-intercept…

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Q: You are given the following pieces of information: 43 f (x) dx = -39, What is the value of 27 ² f…

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Q: Find the general Solution For D-E tan² (x+y) dy

A: The given differential equation

Q: local minima occur on the function, enter in the appropriate box. f(x) = - 23 - 4x² +15x-8 3

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Q: -ind the curvature of r` (t) = ti + t²j + t³ k at different valu oft. Which formula would you use to…

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Q: Use the ratio test to determine whether an+1 lim n→∞ an (a) Find the ratio of successive terms.…

A: Consider the series

Q: Solve the following integration :- 5 (x-3) (x+5) (x-2) dx

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Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

A: The graph of derivative  is given below. To find the interval(s) on which the function  is concave…

Q: The function G (t) = 30 – 8.8 cos (t) models the depth, in feet, of water t hours after 9am. Find…

A: G(t)=30−8.8cos⁡(π4t)Using the power Ruleddxxn=nxn−1ddxcos⁡(ax)=−asin⁡(ax)

Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

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Q: 16 [FIX, F(x, f(x, y, z) ds. S Evaluate f(x, y) = 7y - x S: r(u, v) = cos(u)i + sin(u)j + vk π us T,…

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Q: Calculus 1

A: z=2x2+xyx=cost, y=2sint

Q: Consider the following. y 16 8 0 y = f(x) 8 O R6 16 (a) Use six rectangles to find estimates of each…

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Q: An aluminum can is to be constructed to contain 2600 cm³ of liquid. Let r and h be the radius of the…

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Q: In each of the following functions is there any value of x where the function is discontinuous? If…

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Q: Find all relative extrema. Use the Second-Derivative Test where applicable. (If an answer does not…

A: To find all relative exrema of the following function.

Q: 10 [²0: 9x - 1 x²(x + 1) dx = - [ ²010 dx - [10 / / + dx - 1²0 x 140 1 dx +

A: I=∫1109x−1x2(x+1)

Q: 1. Evaluate each of the following derivatives. You need not simplify your answer. (a) √t (2-1)³ dt d…

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Q: 4. Consider z = ²-y tan(x); x = s/t, y = s²t², use appropriate chain rule to find Əz/at.

A: Consider , by using appropriate chain rule to find ..

Q: Your velocity is v(t) = ln(t² + 1) ft/sec for t in seconds, 0 ≤ t ≤ 2. Find the distance traveled…

A: Velocity is v(t)=ln⁡(t2+1)ft/sec for t in seconds, 0≤t≤2.

Q: Write an integral in the form A = the area of the region. Answers should be exact. As a suggestion,…

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Q: Sketch (on your work paper) the graph of a single continuous function f(x) that meets all the…

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Q: Question 2 Suppose an > 0 for n≥1 and lim Wan < 1 n→∞0 What can you conclude regarding 1 an? The…

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Q: Question 7 Use first (a) (b) principles to find the derivative of f(x) = x² + x f(x) = -√√x

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Q: Set up the integral that computes the volume of the region W in R³ bounded by the surfaces z = 0, x…

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Q: B) y(x) = 2+x

A: I have appended the formula used in solution procedure

Q: Find the equation of the orthogonal of the set of the curves and solve the differential equation:…

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Q: 13. If lim f(x) = lim g(x) = + ∞o and f'(x) = 1 and g'(x) = ex, what is lim 818 x480 x → ∞ g(x) A.…

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Q: Consider a system of 3 equations with 3 unknowns. If the augmented matrix has been correctly reduced…

A: Here we have to general results for finding the solution

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for f(x) = x² - 6x on the…

A: F(x) = x2 - 6x Interval [ -2 , 4 ]

Q: Find the Maclaurin series for the given function. 14e x What is the Maclaurin series of f(x) =…

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Q: Step 4 of 6 We now need the coordinates of a point on the tangent line. Find the y-coordinate of the…

A: Equation of a line.

Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and for the…

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Q: The graph of the first derivative of p(x) is shown in the graph below. Use the graph to answer the…

A: The graph of the derivative function is given.The aim is to find the interval at which the function…

Q: Write the given expression as a single integral in the following form. [_^¸ ƒ (x) dx + [* f (x) dx −…

A: To write the

Q: Use substitution to find the Taylor series at x = 0 of the function In (1+5x9). What is the general…

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Q: 10. An electric scooter manufacturer estimates that the cost C (in dollars) of producing x scooters…

A: Given, Where C is the cost of producing x scooters in dollars  We have to find the production level,…

Q: Kevin needs to find the length of the arc of the given curve. He is struggling. Please help him by…

A: given curve

Q: Given the graphs of polar equations: r = 1 and r = - 2 sin 0, (a) Set up the integral that gives the…

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Q: Multiply both sides by x²(x + 1) and combine like terms. Ax(x + 1) + B(x + 1) + Cx² 9x - 1 A = = X…

A: The equation is given by:-

Q: Use Green's Theorem to evaluate the line integral. S 2xy dx + (x + y) dy C: boundary of the region…

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Q: Find the general Solution For D-E dy dx +y secx = COSX

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Q: If 6400cm2 of material is available to make a box with a square base and an open top, find the…

A: If 6400 cm2 of material is available to make a box with a square base and an open top,then to find…