Let F(x) o f(t) dt, where f is the function whose graph is shown. 3+ 2- 1 3 4 9, -1+ -2+

Q: Let g(x) = f(t) dt, where ƒ is the function whose graph is given below. 0.4 0.2 - 3 -0.2- (a) At…

A: Given, gx=∫0xft dt Graph of the function f is shown as: Concept used: A critical point c is the…

Q: Let F (x) (1 + t4)1/4 dt - Then F'(x) =

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Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

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Q: (1) Let g(x) :| f(t) dt. What is g'(x)? a

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Q: 5x The interval over which the function f(x)= e (1+x) becomes continuous is O [-1, 0) O (-0,…

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

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Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: If f(x) = t* dt then f'(x) = f'(4) =

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Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: 5. Find the linearization, L (x) f (a) + f' (a) (x – . a) of the given function "f" at "a". %3D - f…

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

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Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

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Q: Define a function A : C[0, 1] → C[0, 1] by (A(f))(x) = g(x) = | f (t) dt, 0<x <1. (a) Is A a…

A: Given: The given function is by  .

Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: 1 Find f(1) if f(t) dt = x" - x + 2x? – 2, x >1.

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Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

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Q: F- e'さてi -xyでk is non. Conserv ative DTrue O Fulse

A: We have given a vector field ,  F(x , y , z) = x2yz i + 0j- xyz2 k We need to determine whether…

Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

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Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

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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: e If F(x) = | e dt, find F(1) and F'(x). ez

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Q: Let A(x) | f(t)dt where f is the function given by the graph below. 4 3 -1 -2 А(5) - A(9) = to 2, 3.

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Q: x2 (1) Find f(1) if / f(t) dt = x° – x + 2x? – 2, x >1. |

A: use anti derivative to find the solution

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

Q: 1. Let F(x)=√1+t² dt. Find F'(1).

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Q: Let F (x) = (1 + t2)/5 dt - Then F'(x) =

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Q: 4. Let g(x) = f6 S(1) dt, where f is the function whose graph is shown. (a) Evaluate g(0) and g(6).

A: g(x) = ∫0xf(t)dtHence g(x) is the area bounded by the curve f(t) and x-axis with sign.

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

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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: III. Let g be defined by the equation g(x) = dt t²-1 Show that g'(x) = secx.

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Q: Let A(z) = f(t)dt where f is the function given by the graph bele 3 2 1 2 3 4 5 7 1 -2 -3 -4+ A(5)=…

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Q: Calculate the Integral?

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Q: If f(x) = | (t3 + 3t + 1) dt 0, then f" (x) = ||

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Q: %3! Let A(r) = | f(t)dt for the function f(t) graphed below. Evaluate A(x) for a = 2 and 5. 2 5.…

A: Find area under the curve A(x) from 0 to 2 and 0 to 5

Q: Q5 a) If f(x) = ² (1 - 1²) e¹² dt, on what interval is f increasing? b). Find a function f and a…

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Q: x2 ) Find f(1) if / f(t) dt = x° – x* + 2x² – 2 , x>1.

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Q: 2 2t #6) A) Evaluate: t´e“dt

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Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

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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

Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

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Q: 5. Find the linearization L(x) of f at a = 0 f(x) = = 1 = 0 2+x

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Q: dx Suppose y = x4 – 2x + 1, and both x and y are functions of t. If dt when x = -1. dt = 2, find 12…

A: Given Data The equation is y=x4-2x+1. The derivative of x with respect to t is dxdt=2. x=-1.…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: b) Let 2z f(x) = dt t2 +t+2 find the interval at which f(x) is increasing, decreasing, concave up…

A: Given: fx=∫02x t2t2+t+2 dt To Find: To find the interval at which fx is increasing, decreasing,…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.