Find the slope of the tangent line to the given polar curve at the point specified by the value of 0. r = 4 cos(8), e= |ო

Q: Test the series below for convergence using the Ratio Test. n4 0.82 n=1 The limit of the ratio test…

A: The power series is given byRatio test:

Q: A company determined that the marginal cost, C'(x) of producing the xth unit of a product is given…

A: Consider the given marginal cost function.C(x) is the cost function and the fixed cost is $3000.

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A: We have given the graph of a function and A(x) is the area bounded by the graph from t=0 to t=x.…

Q: Find the local maximum and local minimum values of f using both the First and Second Derivative…

A: Explaination of the answer is as follows

Q: Express the point given in Cartesian coordinates in cylindrical coordinates (r, 0, z). A) (³ ( ¹⁄²),…

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 50x² + 3 (a) Find…

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Q: Given that 0. n=0 x= to x = 8 1-12-2 = Identify its interval of convergence. The series is…

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Q: 1 - 3i З 1 + 2i

A: To simplify the following expression.

Q: [Ⓡ 1 x(x + 1) Hint: you can use the partial fractions expansion Evaluate the improper integral dx. 1…

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Q: If ƒ(x) = 3x² – 3eª, find:

A: f(x)=3x2−3ex

Q: Find f'(x). f(x)=(7x+4)(9x-3) f'(x)= (Type an exact answer.)

A: Given, .Rules of derivative:

Q: Suppose that the profit of a company depends on three variables (x,y,z) and is given by the equation…

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Q: Use any method to find the relative extrema of the function f(x) = 20x + 7x7. If there is no…

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Q: Consider the function f(x)=4- 4x², -3 ≤ x ≤ 1. The absolute maximum value is and this occurs at x =…

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Q: find the derivative of a. f(x)=(x^4+3x)^-1 b. f(x)= x / (x^2 + sqare root of 3x)^5

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Q: Use the shell method in calculating the volume of revolving the parabolic mirror about the x-axis.…

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Q: x 6. Differentiate: y = x² + 3x - 1 A. C. x²+1 x²+3x-1 -x²+1 (x²+3x-1)² 0 2x²+3 eldet 10-(x²+1) B.…

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Q: Which of the following statements regarding absolute extrema is/are correct? An absolute extremum of…

A: The conditions for the existence of absolute minima and maxima in a closed interval for a continuous…

Q: Find the critical numbers of the function. (Enter answers as a comma-separated list) f(x) = x3 +…

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Q: Find the absolute extrema of the function over the region R. (In each case, R contains the…

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Q: Use a calculator and evaluate A to the nearest cent. A = $5,000e1t for t= 3, 7, and 10 Ift=3, A $…

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Q: Suppose R is the solid bounded by the plane z = 2x, the surface z = x², and the planes y = 0 and y =…

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Q: Find the area of the region bounded by the graphs of the equations. 16x x² +1² Round answer to THREE…

A: we need to find out the area bounded by the given curves.

Q: Let f(x) = -9x - 1 Determine the absolute extrema of f on [-5, -4]. The absolute minimum of f is The…

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Q: Region: y = 3x √₁+x3 x-axis, 0≤x≤3. √1+x³¹ Rotated about: y-axis

A: To find the volume of the following region.Region: Rotated about: -axis

Q: Let ✈ denote the vector xỉ + y j + z k and a be a fixed positive constant. Compute divF where is the…

A: Let  denote the vector  and  be a fixed positive constant.To compute where  is the vector field…

Q: A bottle of water with temperature 70 F is placed into a refrigerator with an internal temperatu 34…

A: The Newton cooling law surrounding temperaturetemperature of objectproportionality constant /cooling…

Q: Let f(x) = √6-x The slope of the tangent line to the graph of f(x) at the point (2, 2) is The…

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Q: Determine the exact values of each expression for the given value of 0. Do not use a calculator.…

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Q: So 0 xe- dư x²

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Q: Find the absolute maximum and minimum values of the following function on the given region R. f(x,y)…

A: Given:

Q: Examine the graph shown. Estimate the value c guaranteed by the Mean Value Theorem, and also f'(c),…

A: Given graph of function

Q: use the given test to determine the convergence/divergence of the given series.  P series test…

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Q: The function P(x) = -2.5x² + 775x - 9500 gives the profit when x units of a certain product are…

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Q: Graph the following rational function: f(x)= 4x²+10x+4 x²-2x-8 Along with the graph, provide the…

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Q: Given that 1 1-x = M8 n=0 x" with convergence in (-1, 1), find the power series for 1 9-x with…

A: Given that

Q: Use the chain rule to find the derivative of f(x) =6√/9x³ +8x6 Type your answer without fractional…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: A ball dropped from a height of 14 feet begins to bounce. Each time it strikes the ground, it…

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Q: Determine the intervals of concavity and the points of inflection for the following function: f(x)=…

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Q: K Find the area of the region bounded by the graphs of the given equations. y=x² +6, y=x², x= -3,x=2…

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Q: A farmer finds that if she plants 80 trees per acre, each tree will yield 65 bushels of fruit. She…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: to find the open intervals wheref(x) =(x-6)/(8x+7)  is concave upward and concave downward.

Q: Find the first partial derivatives of the function. || f(x, y) = gy

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Q: If cos 22.5° = √A + √B, then, by using a half-angle formula, find A B =

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Q: Solve the following integral: S ln cx) dx

A: The given integral is lnx.

Q: Let f (x) = x³ - 5x² + 3x - 12. Find the following values. ƒ' (0) = f' (1) = f' (-2) = Jal In 3

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Q: The following table gives values of the differentiable function y = f(x). 0123467Y-13-1-4-7-5-4259…

A: If a function is differentiable then it is also continuous.When there is a change in sign of y…

Q: Part 1 of 5 g(-3) - Part 2 of 5 g (3): = Part 3 of 5 g (-2) Part 4 of 5 g (0) Part 5 of 5 g (4): = X…

A: we are given a piecewise function and we need to find out the values of the function at the given x.

Q: Find the area under the curve y = 1/(6³) from x = 1 to x = t and evaluate it for t = 10, t = 100.…

A: To find the area under the curve  and to evaluate it for . Then to find the total area under this…