Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the graph including the directrices and foci.

Q: Evaluate the line integral, where C is the given curve. xy ds, C: x = t2, y = 2t, 0sts 3

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Q: Substitute the values of f(x), a, and b in the Integral from the previous step, and find the average…

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Q: ||r(t) × r"(t)|| ||r(t)||³ Use the formula k(t) = to find k(t). r(t) = 4 cos(7t)i + 4 sin(7t)j + 3tk…

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Q: Find the conservative vector field for the potential function by finding its gradient. g(r, y, :) +

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Q: Find V. (V × F), if F(x, y, z) = 3e²*i+9xe*j – 4ev*k V· (V × F) =|

A: Use the curl and divergence for the F.

Q: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: A) y=3x^2+3x B) y=(e3x+e-3x)/2 C) y=log5(tanx).

Q: The length of the curve determined by equations x = t² and y = t from t = 0 to t = 4 is %3D %3D %3D…

A: The objective of the question is determine the length of the curve.

Q: Match each point in polar coordinates with either A, B, C, or D on the graph. D

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Q: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find dw/s and dw/at by using…

A: Using chain rule and converting function in term of s and t are differentiated.

Q: (3t – 1)66 dt

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Q: 4. S(9x + 33x +22) dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: sin(6x) lim ? 2+0 sin(2x) Does not exist O 3

A: Given problem:-

Q: 10 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx=5 . 8. (A) True (B) False

A: To determine whether the given statement is true or false.

Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

Q: cy?t1) e COSX y2 dy 8- COSX CotX

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Q: Use continuity to evaluate the limit. 8 + Vx lim 8 + x

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Q: 6. What is the general solution of the following differential a²y.cdy d²y equation -52…

A: We need to find general solution.

Q: Q2 Evauate : fx V+1 dx

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Q: what is the exact answer

A: The exact answer was the second last line of the original solution.  So, the exact answer is:…

Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F) = (4(y+2), 4:x, 0)

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Q: sec(0) = cot(0) = (b) y (1, -1) sin(0) = cos(0) = tan(0) = csc(0) = sec(0) = cot(0) =

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Q: Use Disk Method only Find the volume of the solid formed by revolving the region bounded by the…

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Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 4.…

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Q: S 2y(yª – 4)¯³ dy

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x² N(x, y) = x² – 2y (I): (2xy-3x )dx +…

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Q: What is the instantaneous slope of y == at z = 5?

A: for the instantaneous  slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…

Q: Which of the following systems of linear equations has a solution of (-2,-8)? S 8x + 2y = –32 | y =…

A: To determine which of the following systems of linear equations has asolution of -2, -8.1…

Q: Evaluate the double integral SR Sf(r, 0) dA, and sketch the region 5. S V9 – r² dr d0

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Q: . Evaluate the double integral , Sf(r,0) dA, and sketch the region R. 5. 2 S, v9– r² dr de

A: Let's find.

Q: Perform the addition or subtraction and use the fundamental identities to simplify. There is more…

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Q: What is the area under the curve given the parametric equatio x = t3 and y = t° over [0,1]? O 1/8 O…

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Q: 7. Given that tan (A) = and angle A is in 3rd quadrant and cos(B) = – - and %3D 13 angle B is in 2th…

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Q: Would it be more difficult to find the points where there is a horizontal tangent line to this…

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Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

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Q: d 27. dx ], cos t dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

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Q: Find curl (8z i + 9x j + 8y k). curl(8z i+ 9x j + 8y k) = ( i )i + ( i j + ( )k

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Q: Solve the triangle. 3. B. 7. As 38.2° (Round to one decimal place as needed.) (Round to one decimal…

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Q: A- Find Tylor series generated by f(x) = 2* at 1.

A: The given function fx=2x at a=1

Q: 1) Find the first 8 terms of the recursive sequence. =-3 2,a

A: The given recursive sequence is;  an=an-1 - an-2.

Q: 1. Let -7 3 -3 2 C = 4 A = B = -3 -3 Determine which (if any) of the following matrices are well…

A: The solution is given in the nwxt step.

Q: Sx² sinh xdx

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Q: xp - )s ɛ

A: As per the guidelines I can solve only first question

Q: X+3 Q4) Find the integration by using: dx 2x3-8X

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Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5" %3D

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Q: Fnd the average value of the function over the glven Interval. (Round your answer to three dedmal…

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