Let f(x, y) = 2x² + 2y² - 4y + 9. Then the level curve f(x, y) = 3 is a: Circle with center (1, 0) and Radius R=1. This option None of these This option Circle with center (0, 0) and Radius R=1.

Q: If f(x, y) = x²y + cos(x) then (fx, fy) = (2xy + sinx, x²). Select one: O True O False

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Q: Question 1 f(x, y) = 4xy 2x²+5y² Consider the function a)!* s Find the domain of f. b) [₁ Show that…

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Q: Determine whether the lines L₁ and L₂ are parallel, skew or intersecting L₁: x = 4 + 2t, y = -5 +…

A: L1 : x=a1+b1t , y =c1+d1t , z=e1+f1tL2 : x=a2+b2s, y =c2+d2s , z=e2+f2sthen Lines L1 and L2 are…

Q: Find where it increasing and decreasing x^5-2x^4+3x^2-5x+

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Q: Evaluate (x² - 1)³² dr.

A: Our Aim is to evaluate the integral given below:-∫x2-12 dx -(i)

Q: An equation of the form t²y" + aty' + ßy = 0, t > 0, where a and are real constants, is called an…

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Q: 22. Use the Rational Zero Theorem to help you solve the polynomial equation 2x17x³ +46x²-43x + 12 =…

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Q: J7 -dz 21-8

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Q: A B - f sin(1-x) (2 cos(1-x))4 dx (2-sin(1-x)5+C 5 (2-cos(1-x)5+C 5 O A OB O O D OE None of the…

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Q: Find the general solution of the following differential equation. y" + 4y + 8y = 0 NOTE: Use cy and…

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Q: Integrate: S (2x2-10x+15) gở ba tô 2x + 3 ln() + C ○ 3 ln()+ +C O 2x+3 ln()+ ○ 3 ln() + C +C dx

A: ∫(2x2-10x+15)x2-5x+6dx=∫(2x2-10x+12+3)x2-5x+6dx ∫2(x2-5x+6)(x2-5x+6)dx+∫3(x2-5x+6)dx…

Q: Evaluate: 12+3 2√x+3 ○1-3 ln (7/5) O2-3 ln(7/5) 2 O2+3 ln7 03-In()

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Q: c) I following 1. Determine whether the integral is convergent or not. 10 [." : 6 dx x-6 Vx

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Q: 4 Use the substitution z +9=u² to evaluate √√+9

A: Note: Since, the student has asked to solve only question no. 4, so we are solving accordingly…

Q: Given the function f(x, y) = √2x + y = 1 - x + 1 Select one: O None of those O D= {(x, y)]y > 1 +…

A: To find out the domain of the given function..

Q: 1 x xy 14. JJ j dz dy dx 0x²0

A: We can find the value of the integral.

Q: In(t³ r(t) = 4 lu(t²+1); - (4e-2 - 5e"); _ sin³t 5e²t)j -k, + 1 t3 then the limit lim r(t) equals…

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Q: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

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Q: Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 5x1 + 7x2 ≤ 37 1x1 + 6x2 24…

A: As per the instruction, we will be answering the first one. Kindly post again for others. Given:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 +6, (3, 1) Vf(3, 1) = 2i+…

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Q: f(x, y) = 6√x - y'e a) b) -3xy + Find f and fy. Evaluate fazy (4,-1).

A: Given f(x,y) =6x -y2 e-3xy+3y

Q: ات, 01 +19+₂1 x+₂²0 +19+₂. 1. Evaluate

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Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: sin(tan x) cos²x Evaluate ·[³ dx.

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Q: x+2, The function f(x) = 2x², Select one: Ⓒ True False x≤1 1<x<3 is continuous from the right at x =…

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Q: Evaluate the definite integral by the limit definition. L (x² + 4) dx X 31

A: use the limit formula for integration

Q: Which of the following is the partial derivative with respect to x of the function f(x, y) = 2y sin…

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Q: 2 Evaluate f 9t2 (t³+1)ž Answer: 3 dt.

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Q: 1 Give the antiderivatives of X The antiderivatives of 1 2 are

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Q: 10. Given the complex function 1+z z² Evaluate f (₁¹) A. 1 + 3i f(z) = B.-1-3i = C. 1-3i D. -1 + 3i…

A: Given that a complex function - f(z) = (1+z)/z. And we find f(1/(1-i)). Here i = "iota" that is an…

Q: 5. (x² + y² + 1)dx - 2xydy = 0

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Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: If y = x?, then dy = a Ο 2 Δε Ο 2 Δy Ο 2 Δε Ο π*Δy

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Q: After successfully passing the Technical Written Examinations, you're now at the PRC Main Office ta…

A: Given: there are 5 registrations specialist on different windows faciltaiting registrations, the…

Q: 2. If z = x+iy = (x, y) then (2,-3)(-2, 1) is A. (1,8) C. (-1,-8)

A: Given,             z = x + iy = (x,y) To find   (2,-3)(-2,1)

Q: Suppose that the concentration (measured in gm3) of nitrogen in the soil along a transect of land…

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Q: A screen saver displays 3 cm x 5 cm and then expands it in such a way that the length of the longer…

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Q: What is the equation of the tangent live the When X = 4 √(x) = ² -6√x cheve f(x) = 3/

A: Given ::fx=8x-6xx=4

Q: E A4 sin (e-² + ln z) + C 4 sin (-e-²) + C B O A § 4 (½ − e¯²) cos (e¯² + Inz) dz B E None of the…

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Q: 8. Find the first two non-zero terms of the Taylor expansion for function f(x)=sin x and a given…

A: Let's solve.

Q: Evaluate: St dz 2√√7+3 ○1-3 ln(7/5) O 2-3 ln(7/5) 2 2+3 ln 7 03-In()

A: Given :∫14dx2x+3

Q: dz Evaluate: 5 10+2% 0 1 O Divergent 00 0-1 15

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Q: Question a) b) Let f(x, y) = 2√x - y²e-²xy + ²/3. Find fx and fy. Evaluate fxxy(4, -1).

A: Given: For (a),     ∂ ∂ x2x-y2e-2xy+2y=∂ ∂ x2x-∂ ∂ xy2e-2xy+∂ ∂ x2y=1x--2y3e-2yx+0=2e-2xyy3+1x    ∂…

Q: z = e Select one: True False In (2-y), dz and x = s² - 6t, y = t - s, then the value of when t = 4…

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Q: None of the other choices 7 The curve y = f(x) has the horizontal asymptote y = Select one: 00 1…

A: Given function:- f(x) = (x+35)/(x-5)  To find:- Horizontal asymptote of f(x)

Q: Starting from the same point, Angela starts walking eastward at 6 m/min while Jessica starts running…

A: Please see the below picture for detailed solution.

Q: Question a) b) 2xy Consider the function f(x, y) = 4x²+5²- Find the domain of f. Show that the limit…

A: To find out the domain

Q: 3) [3 Consider the DE: -(4x³y – 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is…

A: For a differential equation Mdx+Ndy=0  to be exact if ∂M∂y=∂N∂xand solution of a exact differential…

Q: Explain (in words) what transformations it takes to transform the function f(x) = x³ into the…

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Q: Find for y = dx dx X [11tªdt. 0

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