f(x) = e-X, [0, 2]

Q: 1. If f(x) cos(t) dt, then f'(x) =

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Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: Show that E [x(t)] = 0. %3D

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Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: Find both first partial derivatives. f(x, y) = √ (x2 + y2)

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Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

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Q: If f(x) • cos ( z ) t'dt then f'(x) =

A: We can find the answer as below

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Find all second partial derivatives of the function f(x, y) = xy + x° + y at the point xo = (2,4). =…

A: Consider the case of a function of two variables, f(x,y) since both of the first order partial…

Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: Find the first partial derivatives of the function f(x, y, z) = xz – 5x²y³z*.

A: Find the first partial derivative of function f(x,y,z)

Q: Find both first partial derivatives. g(x, y) = ln√x2 + y2

A: Given function is gx,y=lnx2+y2 Partial derivative of function is derivative of function with one…

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: Differentiate the function. y=In(x²+e' y=In(x²+ean x)

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Q: What is the mixed, second order partial derivative of this function. f (x, y) = / 2x² + y²

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Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a 6

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Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: 4. F(x) = (1- t) dt %3D 4

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Q: (a) Find the linearization of the function f(x) =x+ at x= a=1

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Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

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Q: (a) f(x) = e" centered at r = 0.

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Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: F(x, y)= x²y?

A: Consider the function  s=f(p, q),here p and q are independent variables and s is a dependent…

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: Find all first partial derivatives. f(x, y) = 4x2 − 2xy + y2

A: Consider the given function  fx,y=4x2-2xy+y2

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: Find the first partial derivatives of fx and fy of the function f(x,y) = 4e2x - x3y5

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Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

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Q: Find the linearization of the function f (x) = a° at a = 1.

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Q: Differentiate the function. y = In(e-X + xe¬X) y' = II

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Q: Find the first partial derivatives of the function. x5 - y5 x° + y f(x, у)

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Q: Compute f -f(g(x)), where f(x) = x° and g(x) = 8x – 1. dx -f(g(x)) =| dx

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Q: Find both first partial derivatives. h(x, y) = e−(x2+y2)

A: The given function is hx,y=e-x2+y2. To find the partial derivatives. Solution: The given function is…

Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

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Q: Calculate the derivatives of all orders: f'(x), f"(x), f"'(x), f(4)(x), f(x) = e3x - 1 f(x) = 3e3r-1…

A: We use chain rule to find these derivatives