Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4
A: According to question, Local linear approximation,lx = x2 +π4-12, .......1Given Function,fx…
Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?
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Q: 8sin 7xcos7y =7 30. Differentiate with respect to t (x and y are functions of t
A: Given equation is 8sin7xcos7y=7 where x and y are function of t. Differentiate both sides with…
Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect
A: The solution is given as
Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.
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Q: 2²y. 3. Consider the function f(, y) =
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Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In
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Q: A function (f) is homogeneous of degree • if and only if : ôf + y = Af (x, y). Does the function…
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Q: Which of the following is a parameterizatino of the line that passes through the point (5, 4) With a…
A: Let's find.
Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…
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Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…
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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)
A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for…
Q: 5. Use Cauchy-Riemann conditions to determine which of the following functions are differentiable…
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Q: Which of the following is a parameterization of the line that passes through the point (1, –3) with…
A: First frame the equation then verify all the given option.
Q: If we approximate f(2)=3.4 using the tangent line, where f'(2)=4, f"(2)=-3, then is this…
A: Clearly from the above statement as second derivative is negative so the actual value is less than…
Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…
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Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…
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Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…
A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…
Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.
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Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2
A: Using leibniz rule Explanation is given below....
Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a 6
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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)
A: The objective is to verify the conclusion of clairaut's theorm.
Q: Assuming that the following equations define z an implicit function of x, y and, z = f(x, y), for æ°…
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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: نقطتان )2( Suppose u and v are differentiable functions of x. Use the given values of the functions…
A: We will find the derivative using formula and the evaluate the derivative of the ratio (u/v) at x =…
Q: Show that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation =0
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Q: 1. The slope of the tangent line for the function f (x) = In x at x = 1 is: (A) (B) 1 (C) 0 (D) None…
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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: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…
A: The given data is: x2+y2+z2=4 To find the value of dzdx
Q: 10.Show that F(x, y) = (1 + xy)e*yi + (ev + x?e*y)j is conservative and find a function "f" such…
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Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…
A: Explanation of the solution is given below...
Q: find the length of the function over the given interval x=2y, y=-1, to y=1
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Q: Suppose f( – 1) = 2 , f'( – 1) = 3 , and g(x) = r'f(x). The tangent line to g(x) at z 1 is given by…
A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…
Q: 2. Let f(x,y)= xe" and find a) fu. fy» fy
A: Please refer the attached image for complete solution.
Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…
A: It is observed that z=fx,y is function of x and y.
Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4
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Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…
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Q: 5 B) Find y" for the function y = x + Vx at p(1,3)
A: Given query is to find the double derivative of the expression at point p.
Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…
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Q: 2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.
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Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe
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Q: Find a function f(x) whose linearization would help me come up with an approximation to 4 26
A: We want to find the function, It's form is ,L(x) = f(a) + f'(a) (x-a) We approximate 4/26 ~ 4/25…
Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.
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Q: 14. If X has the PDF f(r) = 1/4, -1<r<3, zero elsewhere, find the PDF of Y %3D
A: Given,f(x)=14 ; -1<x<3Y=X2
Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.
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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…
A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…
Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…
A: Wr have to find the derivative of the given function first.
Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D
A: Given query is to find statement is true or false.
Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).
A: For the solution follow the next step.
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- As a particle moves through the first quadrant, itsxandycoordinates are functions oftimet, and its polar coordinate θ is also a function of time t.(in function notation:x(t),y(t), andθ(t) ) Given the relation tan θ=y/x take the derivative of both sides of the equation with respect to t to obtain a related ratesequationFind the equation of the tangent line T to the graph of f(x) = 8 sinx at the given point (6,8 sin 6). a. y = (8 sin 6)(x+6) + 8cos 6 b. y = -(8cos 6)(x-6) +8sin 6 c. y=(8cos 6x)(x-6) + 8 sin 6 d. y = -(8cos6)(x-6) + 8sin 6 E. y =(8sin6x)(x+6) + 8cos618.) Let f(z) = 10z + 1 - 15e x . Find the equation of the tangent line to the graph of f(x) at the point (0, —11)
- 3. Consider the function f(x) = e^x2−6x+5. Find the value(s) of x at which the tangent line ishorizontal.Substituting t=0 for the inital equation qoul get <-1,02>, and again with the derivative foem, which would get <0,0,0>. Is that right?Suppose u and y are functions of x that are differentiable atx = 0 and that u(0) = 5, u (0) = -3, y(0) = -1, y (0) = 2.Find the values of the following derivatives at x = 0.
- find a particular solution yp of the given equation. primes denote derivatives with respect to x. y"+9y= 2cos3x+3sin3x1. If f(x) = (2x)cosx, then f'(x) =? 2. If f(x) = sec-1(√(x3+5)), then f'(x) =? 3. find the slope of the tangent line to the curve xy6=ex^5 at the point (1,e).b) Find a function f(x) such that both f′(x) = cos(x) + e^2x + 2x and the tangent line tof(x) at x = 0 is given by y = 2x + 4.
- find a linearization at a suitably chosen integer neara at which the given function and its derivative are easy to evaluate. ƒ(x) = x2 + 2x, a = 0.19. Find the derivative off (x y z) = x^3 − xy^2 − zat(1, 1, 0) P0in the direction of A = 2i - 3j + 6k.1) The function, y =sin(5x-3t), represents a traveling wave with height y, position x andtime t.b) When t = 0, where is maximum x in the interval [0,2π]?c) When t = 1, where is the maximum in the interval [0,2π]?d) What is the speed and direction of this wave?