Find the slope of the tangent to the curve y = sin x sinx at x= O a) -1 O b) 1 Oc) 2 d) 0

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: The parametric form of the tangent line to the image of f(t) = (2t², ?,t +2) at t = 1 is L(t) =

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Q: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

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Q: 3. In A XYZ, m ZY = 90°. Which ratio represents the tangent of Z Z ? O zr XZ O zr XY XZ

A: We are given the following triangle. So, here tan∠Z=XYYZ

Q: Let f(x,y)=x^3-cosy. Find the tangent plan for f(x,y) based at (1,pi).

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Q: Apply the method of Implıcit Di fferentiation to find dy in eq (i) angle O=45 with and loPI-r=472…

A: Given, x2+y22=16x2y.....1x=rcosθy=rsinθr=16cos2θsinθ Now diffrentiating the given function with…

Q: Find the points on (t + sin t, t − 2 sin t) where the tangent is vertical or horizontal

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Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: Show that the tangent at P(x,,y,) on the curve -1 Vx+Jy=Ja is yy, ,=a

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Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

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Q: What is the length of the curve x = cos t + t sin t, y = sin t – t cos t, (0 < t < 2x) ? Lütfen…

A: First I have written the Arclength formula for the parametric curve , then using that formula and…

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

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Q: Find the tangent line equation to the parametric curve x = cos t y = sin³ t at t = V2 O A. y = -x +…

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Q: Find the speed of the cycloid c(t) = (4t −4 sin t, 4−4 cos t) at points where the tangent line is…

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Q: Find an interval of t-values such that c(t) = (cost,sin t) tracesthe lower half of the unit circle.

A: Consider the given point as ct=cost,sint

Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

A: First find derivative then equation of normal line ,and point of coordinate axes and then use…

Q: 4. Use the arc length formula to show that the length of a linear function f(x) = mx +c on the…

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Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

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Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

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Q: Find the equation of the tangent to the curv e y = 23 Az-12 at the point where a = 3. Answer:

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Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

A: Slope of tangent is equal to dy/dx.

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

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Q: Prove that all normal to the curve x =acid+at sin t, Y=a sin t-atcost.Are at a distance a from the…

A: We need to prove that normal to the given curve are at a distance of a from origin.

Q: x² = y + 3y.

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Q: e, Find at the giren point on eauation Of the tangent live. to the corve. X=46",y=f'+|,(4,0)

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

Q: The parametric form of the tangent line to the image of f(t)=⟨4t2,5t,t−2⟩ at t=3 is L(t)=

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Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Find the tangent line equation to the parametric curve cos t y = sin t at t = O A. y = x+ O B. y =…

A: If the parametric equations of a curve are given variable t, then the slope of the tangent is the…

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

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