10. Find the length of the curve defined by x = Vt, y = 1 – t from t = 0 to t = 5. %3D

Q: Find the slope of the tangent line to the curve y = x e at (0,0 e°). dy dx (0,0 e 0) (Round to two…

A: Solution written in details below

Q: 1. Find the rate of y with respect to x at the point (1, 7) if 7y – ry = 4. dy da

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Q: 23. Evaluate Jcxy dx + (x + y) dy along the curve y = x² from (-1, 1) to (2, 4).

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Q: 8) Suppose y log3(xy) = y² – 6x. 8.1) Find at (1,3) 8.2) Find the tangent line to the curve at (1,3)

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Q: Find the curve y(x) that minimizes the I Cy) = S. cos x)+ ]2 Cunc tonal %3D

A: solution:-Given I=∫1+cosx+y121/2using Euler's equation ∂f∂y-ddx∂f∂y'=0sincef=1+cosx+y121/2is…

Q: se implicit differentiaion to find dy/dx for the curve below. 1. xy3 + 4x2 = tan y2 + 3

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Q: Q.1. Justify why the level curves very close to the origin (0, 0) for the function f(r, y) =…

A: To find the level curves, equate the function fx,y with a constant C.

Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

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Q: The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where…

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Q: Given xy + cos(xy) – 4x 5, answer the following: Write the equation of the normal line to the curve…

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Q: 1. Find the rate of y with respect to x at the point (5, 8) if 7y-ry 4. dy da

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Q: Find the rate of change of the distance between the origin and a moving point on the graph of the…

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Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

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Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…

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Q: a. y = cot¯(Ve") tanh(e") -1

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: If the PSD of X(t) is S„(@). Find the PSD of dX(t) dt

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Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The rate…

Q: -1 The tangent line to the graph of y = tanh (4x) is parallel to z + y = 5 at point(s) where

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Q: Find the approximate value of f 10. ' to 4 decimal places using e su

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Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

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Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: Given,   x2+y2=45To find dydt, when dxdt=-2 and x=3

Q: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: 23. Find the normal to the curve x2 + y² = 25 at (4,3). %3D

A: Find the normal to the curve

Q: 29. Differentiate the following implicitly to find dy/dx. Then find the slope of the curve at (1,…

A: Given: x3+y3=9 To Find: Differentiate the following implicitly to find dydx.Slope of the curve at…

Q: What is the equation of the normal line to the curve y = cos æ at the point (6,0) ... A y = -x +; 2…

A: Given:- y = cos(x)  To find:- Equation of normal line on given curve at point (π/2 , 0)

Q: 8. Find ihe point where the normal to y = x + Vx at (4,6) crosses the y-axis.

A: Given :- Equation of line that is y= x+x              The point from which we need to find the…

Q: Q2/ Delermine area boundled by the curve x'+2x'y²+y%_8x°+8y= 0 t. |

A: Step:-1

Q: To find the size of order that will produce a minimum cost, begin by finding the derivative of…

A: To find the value of x at which C has minimum value. C=3x+600,000x

Q: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: A curve is defined implicitly by the equation x²+xy+y? =1 dy Differentiate implicitly to find dx

A: here we use basic differentiation form.

Q: 10. Circles tangent to the x-axis. Amm. (1+() =[yy +1+(

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Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: A curve is defined implicitly by the equation x² + 3xy + y² = 1 Differentiate implicitly to find dy…

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Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

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Q: What is (V | and find the relative minimum dx point as indicated by the black dot on the graph at…

A: Here we have ;  y=xx ..................(1) taking log both of sides

Q: Find dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 < t < π   For which values of t is…

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Q: 10. Circles tangent to the X-axis. Amm. [1 + (y)*]° =[yy +1+(]".

A: Every function can be described through a differential equation. The differential equation defines…

Q: If x = t- sin t and y = 1- cost dy find the dx

A: Given, x=t-sinty=1-cost       Find: dydx

Q: 1. Find the average rate of change in y with respect to x over the interval [1, 7]. 2. Use the…

A: Given that: The function is f(x) = 4x -3 .

Q: with x=sec t and y=e". Then the value of dz evaluated at dt If z=tan In t= 0 is equal to (Correct to…

A: Given function z=tanln4x2y with x=sect and y=e2t Substitute the x=sect and y=e2t in the given…

Q: 3. Find the length of the curve given by : = (y/4)² – 2 ln(y/4) for 4 > y 2 12.

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Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: (3) Find the equation of tangent to the curve given by x=d cos' o y=a' sin'e at point o- VE (x+ y)…

A: Given the equation of curvesx=a3cos3ϕy=a3sin3ϕ

Q: Find the equation of the line that is normal to the curve x cos(xy² – y) = (x + y)² at the point…

A: here option c is true

Q: 3 If the length of the curve y = 4 xž from the point (0, 0) to the point (xo, f(xo)) is L = ((20737)…

A: Given,          The length of the curve y=4x32 from the point 0,0 to the point x0,fx0           is…

Q: me Determine the equation of t e 00 te tragen ܘܪܐܐܝ tangent line to y 3- 22+1 at 2:

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