8 Consider the function y= f(x)= a) Find the quintic (degree five) approximation to f(x) centered at x = 4.

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: Find the linear approximation to the equation f(x, y) = 5 ln (x* – y) at the point (1,0,0), and use…

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Q: 7. The point of contact for a tangent to the curve f (x) = º is (2,4). It intersects the x and y…

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Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: Where is the function f(r+iy) = 4y – 5ix differentiable? Where is it holomorphic? Determine it:…

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

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

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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: 1+x (a) Find the approximation of f, dx using Simpson's rule with step size h 1+x2 0.25.

A: The solution is given as

Q: An object moves along the x-axis so that its position at any time t > 0is given by x(t) = cos(t2…

A: Given :                          x = cos t2+1      , t≥0To find velocity V = dxdt

Q: 10. Find the equation of the tangent plane at (1. 1. 2) for the function f(x,y) = /6 – x² - y'· %3D

A: Here given function as fx, y=6-x2-y2 or  z=6-x2-y2 .....1

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

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Q: Find the point on the curve r(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13π units along…

A: The smooth curve is rt=12sinti-12cost j+5t k at a distance L of 13π units a curve from point…

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

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Q: 3. For the function h(x, y) = x2 + y2 - xy+x find h and h, and then find the tangent plane to h(x,y)…

A: To solve the following problem, We use the standard formula of differentiation and  after that we…

Q: II. Consider the function g defined by 9(z, y) = cos (7z/T) logg(z Do as indicated. In what…

A: We know that the gradient of the function g contains the two vectors, one in the direction of x-axis…

Q: Consider the curve f(x)= sinx - cosx + 1 i) find f'(x) ii) Hence or otherwise, find the maximum…

A: f'(x)=differentiates f(x) w.r.t x

Q: cal linear approximation of f(x) = √ (1+x) at x0 = 0. Use your approximation formula to approximate…

A: The given function is f(x)=1+x at x0=0 we have to Find the local linear approximation.

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

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Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

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Q: 6. Find all values of x in the interval [0, 2 n] for which the slope of the tangent to y e* csc(x)…

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Q: 5. Express the curve by an equation in x and y. x(t) = 2- sin(t) y(t) = cos(t) a. (x-2)² + y² =1 b.…

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Q: 6. Find where the velocity of a particle is zero if its position function is x(t)= t In t

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Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: ンポー、さーポナス 2 an equction of the line tangent too X=t-1 y=t+t the point corresponding Find at to t=2,

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Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: For function y implicitly defined by the equation 3 cos(y) = x + 2y + 4, find its linear…

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Q: Use Taylor's formula at the origin to get a cubic approximation of the function: f(x,y) = ln(2x + y…

A: Given function f(x,y)=ln(2x+y+1) and a,b=0,0 Taylor's expansion  at origina,b=0,0 to get a cubic…

Q: 2) Consider the function y= f (x) = 3{/x. a) Find the cubic approximation to f(x) near x=8. T,(x) =…

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Q: 3) Find the slope of the curve defined by f (x) = x° sin x at x = T. 4) Differentiate g(x) = e* .

A: The slope of a curve y=f(x)  at a given point x=a is the value of dydx  at the given point x=a. So…

Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: Q2\A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Given that,

Q: 5. Find G(1), G'(0), and G'(1/4), where G(x) = | tan t dt.

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Q: Find the absolute extrema of the function y tan( on the closed interval [0, 2]. %3D 8.

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Q: 4. Find and sketch the domain. (4a) f(x, y) = ln (x² + y² – 4) (4c) f(x, y) = /9 – a² – y? V16 – x²…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Use Taylor's formula to find a quadratic approximation of f(x,y) = 9 cos x cos y at the origin.…

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Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 2³ + xe² =…

A: Given function z3+xez=2-y3+lny3 cos(y+1)

Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

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Q: 7 Find the value of c such that the line y =-x + 7 is tangent to the curve y = cyx. 4 с 3

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Q: Consider the step size h = 0.1 and h = 0.001, how does the step size affect the accuracy in %3D…

A: Given that, A=82, B=16.4f(x)=Aex+Bx2sinxFor the given values of A and B,f(x)=82ex+16.4x2sinxWe need…

Q: 5. Find y' at the point (0, e) where xy² + In(x² + y) = 1.

A: Find y' = dy/dx At point (0, e)

Q: 11. Find an equation of the tangent to the curve y = In(4 + x") at the point %3D 12. i) Find the…

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