Consider the function QA1P05 D7E3IJOA1P05 D7E3 f(2) = { if 0 < z < 3 | æ² – 5 if 3 < x Now let QA1P05 D7E QA1P05D7E3IJO P05 D7E QA1P05D7E3IJO g(x) = f(1) dt. Calculate A1P05 D7 IP05 a) g(2) =| JOA1P05D7E3IJOAIR b) g'(2) = |

Q: Let H(x) = | V49 -P dt dt, for - 7sxs7. a. Evaluate H(0). b. Evaluate H'(6). c. Evaluate H'(7).

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If f(x)= J- t2 –1 -dt , find f'(x) t² +1

A: ∫dxx2+a2= 1atan-1xa And  ddxtan-1x=11+x2

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

A: Given function is

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A:

Q: Suppose f= f(x) satisfies f(1) = 7 and f(1.002) 7.008. Estimate the value of at x = 1. dt %3D

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Q: Find F'(x). F(x) = dt t4

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Q: Does the given equation F(y; x) = x° - 2a²y+ 3xy- 22 0 define an implicit function around the point…

A:

Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: Let F (x) = (1 + t2)/4 dt - Then %3D F'(x) =

A:

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

A:

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

A:

Q: Compute the indicated values of the given function. h(t) = V2 + 2t + 25; h(-5), h(0), h(5) %3D O…

A: From the given function: h(t)=t2+2t+25 So,  At t=-5. h(-5)=-52+2-5+25=25-10+25=40=210 Therefore,…

Q: If f* f(t) dt O 6 1 O -4 divergent = 20x √4x²+21 ∞ -4, then f(t)dt is X

A: Given

Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

A:

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: The linear transformation Dx:C'a,b→Ca,b maps a function fx to its derivative Dxf. Here, given that…

Q: Find the function f(x) and all values of c such that

A: To find the function f(x) and all values of c such that∫cxf(t)dt=x2+x-2

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

A:

Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: Express W as a function of  t , where  W(s)=s^2−1  and  s(t)=2t.

A: Given equations - W(s) = s2-1               .....................(1)s(t) = 2t…

Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

A:

Q: If f(x) = t°dt then = (x),f

A:

Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

A:

Q: A. Find and classify all the critical points of the following function: F(x,y)=(3x +4x)( y²+2y)

A:

Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

A:

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: If f(x) = t°dt then f'(x) =

A: We will solve the following.

Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

A:

Q: Find the best linear approximation to f on  the interval [-1,1].                        f(x) = x2

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Q: Find and classify all critical points of the function f(x, y) = x³ + 2y4 - In(x³y³)

A:

Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2

Q: If f(x) = t*dt then f'(x) =

A: Let, Substitute this in the given integral.

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A:

Q: 2. Use a linear approximation to estimate V1.03. 3 If f and a are the functions whose gronhs

A:

Q: Find the linearization of L(x) of f(x) at x=a f(x)=StartRoot x2 +17, End Root a =8

A: Given function and point is

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A:

Q: Find the linearization L(x)of the function at a .

A:

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

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the g'(x) if: g(x) = 1 +t² dt 3x2

A:

Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Suppose that i f(t) dt = x2 - 2x + 1. Find f(x).

A: Consider the following equation: ∫1xftdt=x2-2x+1 fx=ddxx2-2x+1=ddxx2-2ddxx+ddx1=2x-2+0=2x-2

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Q: Obtain the function x to minimize the following functional. x(0) = 2, x(t,) = 5 – 4t

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Q: Let a = f f(t)dt. Find (9-1)'(a).

A:

Q: Suppose you know that: • f(0) = - 18 f(1) = -17 • ( f (y) et dy = 10 Evaluate: [ = f'(t) et dt

A:

Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.