5. f(x) a=-2,2 2 √4-x2 -2 x<-2 -2 2

Q: Find the Cartesian coordinates of the given point. (-4, -1/3) ○ (-2,2-√√3) (2,2-√√3) (-2-√√/3,-2) Ⓒ…

A: First I have written the Cartesian coordinates of a polar coordinates rule, just use it for given…

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Q: A curve with polar equation represents a line. This line has a Cartesian equation of the form y = mx…

A: To write the given equation in the form of y  = mx + b.

Q: = Write the Taylor series for f(x) Find the first five coefficients. Co= C1= C2= C3= C4 e about x =…

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Q: d the area inside ²4 sin 20, 8 4 16 0≤0≤

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2√x + +√x dy = Need Help?…

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Q: Find the volume of the solid generated when the region enclosed by the given curves is revolved…

A: This question is based on application of integration.

Q: Evaluate the ff. limiti. Uning of "L'Hospital' rule is not allowed lim √1-x + 2x + 7 x>-∞ √√9x²+5 -…

A: To evaluate the following limits without using L'Hospital's rule.1 limx→-∞ 1-x+2x+79x2+5-32 limx→1…

Q: 1. lim x→-1 2. lim x →-00 1+ x 2x²+x-1 :-√√x² √√x² + x x- 2 x - x

A: Given:     limx→ -11+1x32x2+x-1

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A: Since the numerator is positive and the denominator x^2 approaches zero and is greater than zero for…

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Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

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Q: Homework 11 Parametric: Problem 3 Suppose a curve is traced by the parametric equations as t runs…

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Q: h₂ = = 3.75 sin(736t) + 7.5 and h₂ = 3.75 sin(736(t + 4))+ +7.5

A: answer of given question is in next step

Q: Q₁: Revers the order and Evaluate in 는 I S dx dy y

A: Given integral is ∫-212∫y1-ydxdyx limits are x=yx=1-yy limits are y=-2y=12By inversing limitsy…

Q: (D³ + D)²y = 0

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Q: 2. Find the area between the curve y=-x and y+x²= 2x.

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Q: Part a) Plot the point given in polar coordinates. (-3, 2pi/3) Part b) Find three additional polar…

A: answer is in next step

Q: Find A where R is the region R outside the circle and inside the V=2 Curve r= 4 Sing

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Q: 1/2 y = (4x-3)¹/²₂ d³y 3 dx

A: Third derivative id given.

Q: Find dy. Do not simplify your dx answers cashy (x² + + 7) = x curt y² 1. COS -241

A: As per the instruction, we will be answering only the first question. For (1),…

Q: For F(x, y, z) = (x + yz) i + (y + xz)j + (z + xy) k, find: (a) the curl (b) the divergence

A: To find curl F and div F

Q: Activity 2.2 For the given function sketch the graph; determine if f is continuous at xo and…

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Q: Sketch the region enclosed by the curves x = sin 3y and x = y, and compute its area as an integral.…

A: We have to find the area between the curves.

Q: Verify Green's Theorem by evaluating both integrals √< y² dx + x² dy = [] (ON - 3M) de dA ?х ду for…

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Q: veen y - II [U, 1].

A: We will find the area .

Q: Determine two coterminal angles in degree measure (one positive and one negative) for each angle.…

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Q: PERFORMANCE STANDARD: Formulate and solve accurately situational problems involving limits. GOAL:…

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Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Find the equation of tangent plane to the surface z = ln (3x²) + 2y at A (1,0, In (3)).

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Q: Given the function f(x) = -√√x + √³, find f'(6). Express your answer as a single fraction in…

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Q: 17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Find in terms of x. dx 18. Given y = 5t (3 - t), t =…

A: Let's find.

Q: Evaluate the following. √(x²-2) e¹-6x dx

A: Use substitution method to solve the integral.

Q: Representing a function as a Power Series. Suppose that we want to represent the function f(x) =…

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Q: The index of refraction n of a transparent material is the ratio of the speed of light in a vacuum…

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Q: Evaluate the function at the given values of the independent variable. Simplify the results. g(x) =…

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Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: Replace the polar equation with an equivalent Cartesian equation. r= 40 sin 0

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Q: Find the area of the region under the curve for the given interval. y=x²+x-6 on [1,4]

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Q: We can prove that if D is a region bounded by a simple closed path C in the xy-plane, then the…

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Q: C: rectangle with vertices (0, 0), (2, 0), (2, 3), and (0, 3)

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Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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Q: Find the derivative of the function. f(t) = (9t+ 9)2/3 f"(t): =

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Q: по + y³ =1, Dzy 2. = .:3 _ x+2y x-2y 3. : . + Злаb2, у" У X sla .

A: We can solve this as follows:

Q: -10 -10 8 61 0

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Q: For the given vectors a and b, find the cross product a × b. a = (1, 0, -3), b =(3, 4, 0) axb=

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Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

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Q: Radius of Convergence of a Power Series. (n!)x" Determine the radius of convergence for the series…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If l'Hospital's Rule does not apply,…

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