True/False The curve x = f (t), y = g(t), a

Q: is differentiable at r 2. 2. (a) Using the definition of derivative, compute for the slope of the…

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Q: Suppose L is the tangent line of y 3 tan a 2 csc x at x = Where does L intersect the x-axis? 40 O At…

A: topic - equation of tangent line

Q: Show that cosh r d tanh-(sinh r) dr %3D 2 – cosh?(r) Show that the derivative of y = x* inh= is…

A: Please find the detailed proof.

Q: d) What is the value of the slope between x and y in the xy-plane (i.e. dz = 0) at the point (1, 1)?…

A: Given z=fx,y where fx,y=lnx2+y2.  Find fx,fy: fx=∂∂xlnx2+y2=2xx2+y2fy=∂∂ylnx2+y2=2yx2+y2

Q: Find the firs t derivative of the f anction y=4sin[sselur)] at the Point x= T

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Q: Q1] Find the derivative of f(x, y) = x2e-2y at po (1,2) in the direction of v =i+j. In what…

A: Given thatf(x,y)=x2e-2yP0(1,2) be a pointv=i+j

Q: 9) The table below gives specific values for a differentiable function p(x). Perform a tangent line…

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Q: A particle is moving on xy-plane with position at time t given by ~p(t) = (t2 + 4t,sin (t + π)). a.…

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Q: For the position function s(t) = velocity at t = 0. Time [0, 1] Interval Average Velocity 15…

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Q: B. Find the value of a such that the following function is continuous at every x Sx²-1, 2ах, x < 3…

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Q: Differentiate the function g(p,9) in derivative and differential form. 5. Given two measurements p+…

A: Given that: Two measurements:   p±∆p and q±∆q

Q: 8. The surface of a water wave is described by y 5(1+cosx), for -nSxST, where y = 0 corresponds %3D…

A: Given that the surface of water wave is described by y=5(1+cosx)  for -π ≤ x ≤ π , where y=0…

Q: 3) Consider the curve given by x= e²" , y = 2e' , 0<t<2 (a) Find the equation of the tangent at the…

A: Given curve is  x=e2t, y=2et, and 0≤t≤2.

Q: Q2: The coordinates of a particle in the metric xy-plane are differentiable functions of time t with…

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Q: Sz 3. Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

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Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

Q: Find the length of the curve Y = V - 1 dt, 1 <¢< 4.

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Q: 不! J Fintsh Line

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Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a ,b],…

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Q: Find the derivative of the function at Po in the direction of A. f(x.y.z) = 9 ex cos (yz),…

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Q: a. Differentiate with respect to the parameter t x = sin?t, y = cos²t b. Find the derivative dy/dx…

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Q: 1. Answer the following: (a) If you are given a differentiable function f, give at least one…

A: Increment of the function=differential of the function. for small change of x

Q: 12)Find the derivative of y with respect to z. Y= 6^(z^3) Dy/dx =

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Q: Given the differentiable function y= f (x) you need to find the equation of the tangent line to the…

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Q: The tangent lines which was drawn at points A and B on the following y = f(x) function graph are…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=2 ex cos (yz), Po(0,0,0),…

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Q: Suppose f(r) is a differentiable function. State the formula that determines the length of f(x) for…

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Q: dz Find dz and by implicit differentiation, and confirm that the dy results obtained agree with…

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Q: We must now find the slope of the tangent line at the point of tangency, (1, In 2), by aun buneinɔ…

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Q: 1. Use a linear approximation of the function g(t) = /t at the point t = 4 to approximate V3.9. Show…

A: Linear approximation of the function gt is given by: Lx=gt+g'tx-t

Q: 3. Use implicit differentiation to answer the following about the curve 42²y" – 2r = r° + 4y%.…

A: given :

Q: 2(z–1) sinh z cosh I + 3(x – 1)'sech? (z)? Which among the choices will result to a derivative of O…

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Q: Praw a slope field for the dtfferea- differentiation equation y = xty sketch an and approprlocte…

A: We have to draw a slope field for the differential equation given below: y'=x+y. To sketch the…

Q: Which is not the about f(x) = |x|? Continuow at O no targent line at 0 Derivative from left at O is…

A: Use the function value to evaluate which one is false

Q: 4(a) A curve is defined by x=5cos(t) and y=3sin(2t) on the t-interval [0,2pi]. Find dy/dx and find…

A: Given,          A curve is defined by x=5cost and y=3sin2t on the t-interval 0,2π.

Q: Slope of a tangent line at t1 = 6.0 and y = at? dy v = lim At-0 dt

A: Given that: y=αt2

Q: (c) Use the chain rule to find the derivative of the function z = 2xr*y³ – ry² along the curve given…

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Q: Use linear approximation, i.e. the tangent line, to approximate V8.1 as follows: Let f(x) = a. The…

A: To approximate ³√(8.1)

Q: Use linear approximation, i.e. the tangent line, to approximate 1.3 as follows: Let f(x)=√x. The…

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Q: Let T= f(x,y) be the temperature at the point (x, y) on the circle and suppose that on the circle x…

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Q: Find an equation for the tangent plane to z = f(x, y) at (3,-2) if the differential at (3,-2) is df…

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Q: Find an equatlon of the tangent to the curve at the glven polnt. x - 9 sin(t), y t+t, (0, 0) Graph…

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Q: Find the length of the curve for the interval 1 ≤ x ≤ 9 3 = √ √ √ ² ³ - 1 d dt 1 Select the correct…

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Q: Q#3. The radius and height of a right circular cone are measured with errors of at most 1% and 4%,…

A: Given that: Percentage error in radius of  cone = 1%Percentage error in height of cone = 4%

Q: (i) Sketch (as accurately as possible) below the function y = t², as x varies from -2 to 2. Then…

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Q: AMoving to the next question prevents changes to this answer. estion 1 * at (4, - 4)? What is the…

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Q: A stone is thrown into a body of still water and created ripples in the form of concentric circles.…

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Q: Use linear approximation, i.e. the tangent line, to approximate V64.4 as follows: Let f(x) Vx. The…

A: First, find the equation of the tangent line to f(x)=x3 at x=64 as follows. The slope of the tangent…

Q: Hw.4 consider a ctosed Kectangutar box uith a If base side ir measured with evror at 2% and the…

A: Volume of the box with square base is given by V=x2ywherex=base sidey=height Surface area of the box…

Q: A coat of paint of thickness 0.07 cm is to be applied uniformly to the faces of a cube of edge 40…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: