please both

Q: Given the function below: Approximate the following using h = 0.2: f(x) = ex cos(x²) a. First…

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy…

A: Gievn, x=4t,y=8t And 0≤t≤1

Q: The value of the integral is equal to: Select one: None of them 813113 L. (8 (8x - 8y) dy dx

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Q: Complete the table for f(x) = f(x) Round the values of f(x) to five decimal places. Enter your guess…

A: The given function is;  f(x)=2sqrt(x2+x) /(x+3).

Q: Is the equality true or false? Select one: True False 1 ST 8r sin 0 dr d0 = 0

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Q: Let R be the region bounded by y = 2x, y = 2 and x = 0. Sketch the region R and evaluate the double…

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: Please see the below picture for detailed solution.

Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

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Q: Find the lim inf (xn) and lim sup (x₂) of Xn = COS nπ

A: I have calculated the limits

Q: Use the properties of infinite series to evaluate the following series. 3. 5" Σ n=0

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Q: Evaluate the integral 2-x 2 [²² 0 0 xdydx.

A: Solve the integral ∫02 ∫02-x x dy dx. Concept used; Power rule of integration; ∫xndx=xn+1n+1+c

Q: If you evaluate the integral expression 2x+1|dx the -2 result is Blank 1 (use fraction or decimal in…

A: To find out the definite integral.

Q: Find the gradient vector of the function f(x,y) =. Select one: O None of the others. - O O + 6xy,…

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Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix…

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: Follow the procedure given below.

Q: Find the directional derivative at (1,0) if Vƒ(1,0) = in the direction of the unit vector u = i?…

A: Given : ∇f(1,0)=<-4,3>   To Find: directional derivative at (1,0) in the direction of the unit…

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Given problem:- A farmer is building a fence to enclose a rectangular area consisting of two…

Q: The Integral fi fig(z,y) dyda can be written as: 21-9(x,y) dzdy Select one: O True O False

A: We can solve this as follows:

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: Given the function h(x) below, select the answer choice(s) which correctly decompose h(x) into…

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Q: State the equation of f(x) if D = {x = R | x = }} and the y-intercept is (0,2). x + 1 a) f(x) = 3x+2…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: b) 0 em dac

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Q: 2. A differential equation that is a function of x only O will produce a slope field with parallel…

A: Here, given that the differential equation is a function of x only. So, dydx=f(x)⇒y=F(x)+C, where…

Q: en differential equation by undetermined coef y = x²ex + + 3

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x3 (3x²+2)³ J…

A: Given: I=∫x33x4+23dx     ...1   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Question 1 1 a. [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) =…

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Q: Hint: Analytical answer is required to be uploaded in Moodle 1. Consider the differential equation…

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Q: Work Problem 1 (1 ): Evaluate the double integral where R enclosed region bounded by x = 0, y = 2,…

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Q: (g°N)(x) (fºg)(x) If f(x)= x-1 and g(x)= x², what is the first derivative of (f+g)(x) (g-n(x) +

A: To find out the derivative of the indicated function.

Q: •√ (2x + √₁ (2r+√16-r²) dr by interpreting it in terms of areas. 10. Evaluate

A: Bh

Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² - 2x³ + 3y² + 6xy. b. s]…

A: Extreme Points of Function f(x,y)=6x2-2x3+3y2+6xy

Q: Give an example of a derivable function f (x) with f ′ (- 4) = - 1

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Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

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Q: Evaluate the integral 0 2 0 2-x xdydx.

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Q: 8. Graph the curve and find the area that it enclosed: r = 2 cos(0).

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Q: divergent: Select one: O True False ts) The following series is 8 Σ6- n=1 3 n-2

A: Given: ∑n=1∞6-35n-2

Q: Test the series for convergence or divergence. Select the correct answer. The series is convergent…

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Q: The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula…

A: We need to find S'(t).

Q: Obtain the general solution for the following differential equation using Separation of Variables…

A: Using method of seperation of variables

Q: The demand x is the number of items that can be sold at a price of $p. For x = p2² - 4p +600, find…

A: We can solve as follows

Q: 6. Find an equation of the tangent line to the curve at the indicated point: (t) = t cos(t), y(t) =…

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Q: Obtain an exponential function in the form f(t) = Aet. HINT [See Example 5.] f(t) is the value after…

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Q: Г.Г 0 0 2 2 y dydx = 2. Select one: O True O False

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Q: Find the domain of the vector-value function r(t) = www Domain: {tt # MORA 4t4, t², 1 (t - 2)5

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Q: a) Determine if the geometric series 8n-1 90+1 n=1 is convergent or not, and find its sum if it is…

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Q: Question The series Select one: Σ n=1 is a geometric series with r = True O False 5" -lin

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: In evaluating 4 S²- 2dx -, is same as evaluating lim cos-¹(f(x))|4. Determine the value of of f(x)…

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Q: Find the total mass of the wire with density p. r(t) = cos(t)i + sin(t)j, p(x, y) = x+y, Ostsn

A: Please see the below picture for detailed solution.