4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

Q: 4. Find using derivative rules. dx sinx x8+x x2 tanx (a) y = (b) y= (c) y = cos³(3x² + 9) cos(5 x*)…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: find the directional derivative of f at p in the direction of B.  if f(x,y,z)=x+ycos(z) where p…

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Q: 75. F(x) : (t + 2) dt

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Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: Value of divergence of function (x2y2)î - (z³y 4x) ĵ + 4y² xk at (1, 2, 1) is

A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

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Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: Evaluate using integration by parts: fx sec-¹x dx

A: SOLUTION-

Q: Find i) Partial derivative. tii) of the function i Z= 200+xy Level Sur face エエ

A: Given z=200+x2y2 i) Partial derivative zx=0+2xy2=2xy2zy=0+2x2y=2x2y ii) Level surface of the…

Q: Find the rate of change of f(x,y) = In(x +y +z) – xyz in the direction from (-1,1,1) to (2,1,5) with…

A: solve:

Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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Q: Find F (x). sin(x) F(x) = Jo 3VE dt F "(x) = %3D

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Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

A:

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Find the direction 0 in which the directional derivative of the function x + y f(x, y) = 2(x + y) -…

A: Given that: f(x, y)=2(x+y)-x+yxy

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Find total differential of function u = x.

A: 6. The given function is u=xyz. We know that the total differential of a function u=fx,y,z is given…

Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x&gt;0…

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Continuity equation is derived using the conservation

A: Equation of Continuity: The continuity equation states that in the case of steady…

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

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Q: integral of sqrt(9-x^2)(x)dx. limits are from 0 to 3

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Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: continuous function h(x),

A: Differential equation

Q: The gradient of f(x, y) = e³ ² sin(3 - y) at (x, y) = ( - 1, – 3) is defined as followed: V f(а, у)…

A: It is gradient vector by using partial derivative

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (- 3, 1) and…

A: First find gradient at point and take dot product with unit vector

Q: Find the tangent line approximation for f(x) = v2 – x at x = -2. Use it to estimate the value at x =…

A: Solving using linear approximation formula

Q: -f integration for

A:

Q: The maximum rate of change at a point on a function f(x,y,z) is да ylgr

A:

Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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Q: Find the rate of change of f(x,y) = In(x +y+ z) – xyz in the direction from (-1,1,1) to (2,1,5) with…

A: Given problem is :

Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: /Find the directional derivative of the function (f(x, y, z) = x + xcosz-ysinz+y), P₁(0,1,2). at…

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Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: ind the 9th derivative of f(z)=exp((-1 + isqrt 3)z) at z=0.

A: Given f(z)=e(-1+3)z Differentiating w.r.t 'z' f'(z)=e(-1+3)z(-1+i3) f''(z)=e(-1+3)z(-1+i3)2…

Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

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Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) + y2 + z2 (3, 7, 2)…

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Q: Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: Find the rate of change of f(x,y,2) = In(x + y + z) – xyz in the direction from (-1,1,1) to (2,1,5)…

A: The gradient vector to the given scalar function is:…

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: IT Evaluate the proper integration from 0 to 4 of arctan x. Leave your answer in terms of r.

A:

Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.

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: