|0, -Tくt<0 Find the FS for f(t) = t, 0

Q: If g(s,t) = f(s^2 - t^2, t^2 - s^2) and f is differentiable, show that t(∂g/∂s) + s(∂g/∂t) = 0

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Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: The function F(x) : te dt is cocave down for all x > 0.

A: Proceed as shown below...

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = -√x²+y² is Z- continuous?

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Q: ind the value of x at which F(x) = S(t|+2) dt %3D 3 akes its minimum value on the interval [4, 60].

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Q: IV. Let f(x) = cos x and t e R+. f(x) – f(t) Vrt – t lim 2 =? x→t -

A: If we have one of the following cases, limx→a F(x)G(x) = 00  OR,  limx→a F(x)G(x)  = ±∞ ±∞ where a…

Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: Find Tn centered at x=8 for all n for the function f(x) = ex

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: 1srs0, then (i) Test whether the Rolle's theorem holds for the function f(x)=D< In 0<xsl the…

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Q: Let f : R → (−1, 1) be given by f(x) = x/(1 + |x|). Show that f is differentiable at x = 0, with…

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Q: If f(æ) = S Tm dt for x > 1, 1 | In t find f'(2).

A: Please refer the attached image for complete solution.

Q: Let g(x) = S,"(t² – 3t) dt. On what interval(s) is g concave down? Justify your answer.

A: To find the intervals in which a function f(x) is concave downward solve for f''(x) &lt; 0.…

Q: hich z ∈ C the function e^(1/z) is holomorphic?

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Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: 4. Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin z for x €R is…

A: In the question given that we have to solve any one of them. Let us solve the first one.

Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function.  F(x) = (1 / x) , a = 2

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Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: to verify thiIS 1 For which values of a ER is the function ax? f(x + iy) = (ax- ary) + i + ay 2 an…

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Q: For function f(x,y) to have maximum value at (a,B) IS 1) rt – s>0 and r0 and r>0 3) rt – s?0 and r>0

A: for function f(x,y) to have maximum value at (a,b) is rt-s2&gt;0,r&lt;0

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

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Q: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

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Q: The limit of f(x) = sin(x) as x approaches t is O T/x n/2

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Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: If f is differentiable everywhere and f(1)=f(2)=π, then ∫12 f'(t)dt=0   True or false?

A: True because,

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: 2. For which values of a is f(x) differentiable on R?

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Q: Let f(x) = 2 – x². Over the interval [0, 2], calculate (a) R4 and (b) L4

A: As per the instruction, we will be answering only the first question. For (1), For L4:

Q: Σ sin k+1

A: to show that the given series ∑k=1∞1ksinxk+1 converges uniformly on R to a differentiable function f…

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

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

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

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Q: Let F (x) : tan't dt. Find F' (V3 -1, 4 27

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Q: re3 For x > 1, if F(x) = / 1 dt, then it is the the case that F(x) = In(x) for all x > 1. t In(t)

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Q: Give the linear approximation of f(x) = x sin(nx2) at x = 2. Use this to estimate f(1.98)

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Q: The function f(x) = -elxl - 1 is differentiable at x = 0 Select one: O a. True O b. False

A: The function f(x)=-ex-1. We have to check whether it is differentiable at x = 0 or not.

Q: 3. Given that f(r) = dt. Determine the interval(s) on which f is increasing. %3D 3+t

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Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=3 and f(x) dx=6.

A: Given data: The first condition given is f(4)=3. The second condition given is ∫04f(x)dx=6. The…

Q: The limit of f (x, y) : as (x,y) approaches (0,0): %3D O Infinity O Doesn't exist Exists and equal…

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Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

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Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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Q: what is the limit of f(t) as t approaches 3. F(t)= ((1/t)-1/3)/t-3?

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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,…