Let's practice on how to complete the square because this will help us to identify whether the given equation represents an ellipse, a parabola or hyperbola. Complete the square for the following equations: 1) 2x² - 12x + y² + 6y +26=0 2) 36x² - 4y² - 36x - 8y = 31 3) 9x² +8y² - 15x + 8y +27= 0 4) x² + 4y² = 4x+8

Q: Consider the curve, x² - y² + sin (TX) In(x) + x = 0. =

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

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Q: find the values of λ for which the determinant is zero. 2 λ + 1 0 0 1 O(-1, 1, 1) O(-1, 1, 0) O(-1,…

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Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

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Q: 2x²+x+1 S (x− 1)(x + 1)(x − 2) dx = ₁ 11 (A) 3 (B) None 11 C 3 (D) -SA+ 1 3 E -2 B + x+1 x-2 Q dx,…

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Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: Which of the following is or is not an improper integral? Clearly explain your choice. A. ₂dx B. dx…

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Q: 15. [sec xdx

A: Trigonometric Identity: sec2x=1+tan2x

Q: 50 [" ( ax³ + bx² + cx) dx = 2b = 25 150 x ²6 x²dx -50 0 A) True B False

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Q: What will be the rate of change of the volume of a sphere with respect to its radius when the radius…

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Q: For each function graphed below, state whether it is one-to-one. Graph 1 Graph 2 8- 4- 6+ 2+ 4-…

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Q: Determine the area of region by y = x^2 + 4x and the y - axis

A: Area between the y=x^2+4x and y-axis is unbounded .  So, we will find the area bounded by the region…

Q: Evaluate and Solve the function using the product and quotient rule of differentiation. Show your…

A: Here we have to use the concept of derivatives.

Q: usz 52 и (Inn)" 14 и OF U dim

A: We need to find limit.

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

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Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

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Q: 11. fel/x²di .3 X хр

A: Here, to evaluate: I=∫e1x2x3dx

Q: 3. Use the Intermediate Value Theorem to show that there is a solution of the equation, ³-4x = 1 in…

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Q: 20. (x-2x³+1)dx (x² - 2x+5)

A: I am attaching image so that you understand each and every step.

Q: sec4 w tan w dw

A: Solution of given question is written in below steps.

Q: y dy Find S y+2 O ²(√y+2−5) (5√/y+2−y+24) + C (√y+2−5) (5√/y+2+y+24) + C (√y+2-5) (5√/y+2+y+21) +C 3…

A: A detailed solution is given below.

Q: f(x)= (7x¹-5x-2)

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Q: Laplace Transforms Solve the following differential equation completely without using calculator. y"…

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Q: Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x.

A: As per Bartleby guidelines rule I am answering only first question as other questions are not a…

Q: 5. fx3* dx

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Q: A manufacturer drills a hole through the center of a metal sphere of radius 5 inches. The hole has a…

A: I am attaching image so that you understand each and every step.

Q: 14. sec xdx 2 3/2 (1 – 4 tan x)³/²

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Q: Solve the given function using chain rule of differentiation. Show your full solution.

A: On solving this we will get

Q: 3. f(e-²x - 1) dx

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Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: 7. In drawing 5 cards from a standard deck of cards without replacement, what is the probability of:…

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Q: WW |Q3.If f(x,y)=sin²(x−3y)+sin "¹(xy) s fin 34 and 3 dy

A: Given :f(x,y)=sin2(x-3y) + sin-1(xy)

Q: Find if x-t³+1 and y=4t²-4t. d²y dx²

A: Solution of given question is written in below steps.

Q: [+ dr. sin√xcos√x Зл A 256 3 B 512 None Зл 512 (D E لما 3 256 -dx is equal to

A: We can find the answer as below.

Q: 2. x²+x+2₂ x²-1 -dx

A: Follow the procedure given below.

Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries. 16-y²…

A: Q=∫-44∫016-y2∫0y+6y2z dxdzdyS is the solid of integration of the integral Q.Sketch S and label its…

Q: Applying basic rules of Differentiation. Evaluate and Solve the function using the product or…

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Q: Timothy heard that he could triple his money in 27 years if he invested it in his friend's business.…

A: To find the compound interest.

Q: (2x + 3)dx 9x²+2x+8 17. S

A: Given that…

Q: 17. fe-Inx √√In x² dx 3

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Q: Stoe 0 ex dx Evaluate: A 0 (B) e (C) + ∞ (divergent) D 1 E) None

A: ∫0+∞e-xdx here ∫e-xdx =  -e-x

Q: 1. Find the limit, if it exists.If the limit does not exist, explain why. (a) lim √√²+1²+1+3z² z²+1…

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Q: (D² + 4)y= 4 cot 2x

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Q: Integrate each of the following. Show complete solution. 1. 1000dx 2. S²x¹ + 3x² + 1)dx 3. f(u² + u…

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Q: Find the equation of the tangent line of the function tan (xy²) = 2xy, a J absoleto 700 nu at x = π.

A: Let's find equation of tangent line of given curve at x = pi.

Q: QUESTION 16 y dy Find of- using the substitution +5= √√y+2 √y+2 ² (√√y+2-5) (-5√/y+2+y+21) + C…

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Q: ·S- A 4u B [4-(2u²) ² C) -du V 4u Ⓒ* D -du 4 For x 1/2 -dx and using the substitution u=x1/2, the…

A: We have to solve above integral

Q: 6x⁹-x5+ 27 A B R C D) 0 E) None K|N 2 4-x² dx is equal to

A: Explanation of the answer is as follows

Q: Find y dy ·S- using the substitution +5= √√y+2 U /y+2 /y+2−5) (5√√y+2+y+24) + C…

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