Pपा+ with a focus at co,-1) 'and directrix y=l

Q: Find the work done by the force F = 4xyi + (2x² – 3xy)j by pushing a particle along the line segment…

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Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: If cosh x  =5/3 and x>0 , find the values of the other hyperbolicfunctions at x .

A: Given  cosh x  =53 , x>0

Q: d [arcsin 3x] dr 3 1+9z² 3 1–9z² 1 1+3z2 /1-3г?

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

A: The slope of the tangent is:

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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Q: Differentiate. cosx² + siny³ = 36 %3D

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Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (4,). %3D

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Q: If the functions y = sinx and y = cosx are both subjected to à hórizonlal %3D transformation would…

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Q: where does this concave up and down?

A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…

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Q: The prolate cycloid given by x = 2t − π sin t and y = 2 − π cos t crosses itself at the point (0,…

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Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: PCt) =<5-t, 4t -3,3t7 uking are length Reparami tize parameter from the point (4,113).

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Q: 1. Point K is located at (4. 2, 0. 3)and point Lis located at (5. 8, -0.6). What is the location of…

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Q: Consider the curve C parametrized by x = -1 + 6 sin t and y 6 cos t for -n <t< 9n. %3D Then C is a…

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Q: 9– x² -dx

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

Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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Q: Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an…

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Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: The projectile is thrown at the angle of 45 degrees with the initial velocity of 1 meter per second.…

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Q: Evaluate tanh^2 (4-4i) sech (2+2i). Express your answer in rectangular form in 4 decimal places.

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Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Equations of the curve in the given question is: Slope of tangent line is given by dy/dx, hence…

Q: 44. Find a parametrization of the right branch (x > 0) of the hyperbola 1 - using cosh t and sinh t.…

A: The equation of hyperbola is xa2-yb2=1   The right branch (x&gt;0) of the hyperbola can be…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

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Q: Obtain the dirfferential equation of the family of curves:  1. All circles passing through the…

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Q: What is the length of the arc y = (2/3)(x2+1)3/2 over the interval [3,6]?

A: We need to compute the length of the arc of the given curve over the interval [3,6]

Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

Q: 3. A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35°…

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Q: Sketch one period of y = 2 cos z-1. Make sure to label the y-axis. x Clear Undo Redo 211 FIN

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Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: Compute the length of the curve r-4 sin 26 for Approximate to three decima places.

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Q: Find an approximation using linearization techniques. Please do not use the table of values.…

A: Given, Using the linearization technique to find the  approximate value of sin (3.19)

Q: What do you mean by adaptive quadrature method? Compute cos x dx by adaptive quadrature method and…

A: Composite rules can be used to implement an automatic quadrature procedure, in which the all ofthe…

Q: parametrically

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Q: Regionenclused by the_curve (r=2 cos20)-

A: Given:     r=2cos2θ

Q: a) Find the equation of tangent line of curve that is given by parametric equations x = 3cost + sint…

A: The slope of the tangent at a point on the curve, y=f(x) is equal to the first derivative of the…

Q: the length of the curve y = coshx 1<= x <=2 is sish (2) - sinh(1) Select one: True False

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Q: cosax + sinx = 0, [0.2]

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Q: Find generul solution ý +y tan (x) = see (X) - sec %3D

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Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: 3. Parametrize the circle of radius 5 having centre (8, –3) and hence find a tangent vector and the…

A: We have to find parametric equation, tangent vector and tangent line for the given circle.

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A: Given:

Q: Find the length of the arc of the curve 9y2 = 4x³ from the origin to the point (4, ). %3D

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Q: What coordinate system is suggested if the integrand of a tripleintegral involves x2 + y2?

A: Given: The integrand of a triple integral involves x2 + y2