[a] Use the data from the table to find an approximation for R'(45).

Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: 16. F(m, r) = Gm/r² at (100, 10)

A: We wil use rules related to multi variable calculus to solve this.

Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

A:

Q: Given that the first derivative of x^81+y^81=-36 is given by dy/dx=kx^c/y^c,what is the value of k?

A:

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: Evaluate the derivative of the function r(t)=⟨lnt,3t+1,t2⟩ at t=1.

A:

Q: The total derivative of f(x,y) = e2x +5y is df =

A: Consider the following function: fx,y=e2x+5y Total derivative of function:…

Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: The current in a wire is defined as the derivative of thecharge: I(t)  =Q'(t). What does  ∫ab I(t)…

A:

Q: The linear approximation at x = 0 to sin(9x) is A + Bx where A is: and where B is:

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: What is the value of f (5) if f (t) sin (Ta) dt :? 1

A: Given, ∫1xfttdt = sinπxx   We have to find the value of f5

Q: Consider J(0) = 30* + 1. Let e = 0.001, compute the numerical approximation to the derivative at 0 =…

A: The given problem is to find the derivative of the given function at point 2 with given accuracy…

Q: Find the antiderivative of the given derivative. ds = 5t(212 – 1)3 dt

A: Solution:-  given that  dsdt=5t(2t2-1)3 now  using identity (a-b)3=a3-b3-3ab(a-b)

Q: Use the Quotient Rule to compute the following: t2 +1 d at t = 2 dt t2 The derivative is:

A:

Q: Use the Product Rule to compute the derivative: Find d/dt ((t^2+1)(t+9)) at t=5

A: To find  ddt[t2+1t+9]    at t = 5 Using Product Rule of Derivatives

Q: Find the derivative of this complex function: where z=x+jy (2+jj?

A:

Q: find the general salution of ly-3y12)de = xdy,

A:

Q: Suppose we have the position function: r (t) = t. t2 Evaluate the tangential component of…

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Q: Use the Product Rule to calculate the derivative.

A: y=t-8t-1et+t2

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

A:

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

Q: Use the Quotient Rule to compute the following: d ( t2 +1 at t = -4 %3D dt \ t2 – 1 The derivative…

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Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Obtain dy from the following function y= e v*

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Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

A:

Q: Find the orthogonal trajectories of r^n= a^n cos . given that r(1) = 13

A: Hey there since you haven't mentioned any angle of cos therefore i am assuming it to be cos (n…

Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: Find for the equation below. dy dt

A:

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Use the Quotient Rule to compute the following: d t2 +1 dt t2 – 1 The derivative is:

A:

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: dy dy For the function dt 7 cos t, the third order derivative dt3 is %3D

A: derivative with respect to t first oder derivatinve dydt is ddt(y). (which is given in the…

Q: 51. grad f = (2x + 3e")7 +3xe'j

A:

Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

A:

Q: The linear approximation at x = 0 to sin (7x) is A + Bx where A is: and where B is:

A:

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: f(t) dt t sin(rx), -? What is the value of f(5) if

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given data is : dxdt=5et-3 , x0=4 To find the antiderivative

Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: The linear approximation at x = 0 to sin(7x) is A + Bx where A is: and where B is:

A:

Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

A:

Q: What is the derivative of r(t)=e^(4t)costi+e^(4t)sintj+e^(4t)k

A: Differentiate both sides with respect to t.

Q: 3 dK Use the definition of the derivative to find for the function K(z) %3D dz 6z + 1"

A:

Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

A: