. Let f : [0, 1] R be defined by |-1, z = ; >50 f(x) = {0 |

Q: An RC circuit with a 100 Q resister and a 10^(-2) F capacitor is driven by a voltage…

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Q: Suppose 2 < f'(x) < 6, for –1 < x< 1. Then f(1) – f(-1) is between A) 2 and 10. B) 4 and 12. C) 0…

A: GIVEN : 2 ≤f'(x) ≤6,  for -1 ≤x≤1 TO FIND : f(1) - f(-1) HINT : Mean value theorem

Q: Let f:A-B and X,Y be subsets of B. Then f-¹(XnY) = f'(X) nf-¹(Y). True False

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Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: f:(-2,1]→[0,12] literal and overlapping function 12 if įs(x) dx = 13andſls*(x) đx =5 [f*(x) dx=? 10

A: Given :f:-2,1→0,12 literal and overlapping function.∫-21fxdx=13     →1∫06f-1xdx=5    →2To…

Q: Consider the function f(t, p) 3 (pе' +1—р)". a. Find an expression for f(t, p) and evaluate that…

A: Given that:f(t, p)=(pet+1-p)n

Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

A: Given: fx=5x2-4x+7 for x∈1, 4 To be find c∈1, 4 such that fc=13∫14fxdx Integral of ∫xndx is given by…

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

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Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: If f:[-5, 5 ] to R is a differentiable function and if f'(x) does not vanish anywhere, then prove…

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Q: Provide concise explanations for the answers to the following: c.) Which is greater, f (2) or f…

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Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: the following statement. 'If yes, explain why. If no, provide a counterexample. For every real…

A: If the function is injective , then the above statement is true.

Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

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Q: For the function Hlo>x'tle, fnd a)flxth) 5bf(xth)- flx) c) f(x th)-f(x)

A: Given: f(x)=x2+6 To find: a) f(x+h) b)f(x+h)-f(x) c)f(x+h)-f(x)h

Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: Given z = f(x, y), x= x(u, v), y = y(u, v), with x(2, 6) = 4 and y(2, 6) = 5, calculate zu(2,6) in…

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Q: 5) Evaluate F dr where F(r, y) = ry i + j, , r(t) = ti+ 3t j, 1<t<4 %3D

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Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: for If f (2) is a regular function of z, prove that f (2) 2 = 4 | f'(2) 1?. %3D ve I f12) 1? =4 |…

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Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Let f(x) = x° – 2, -1< x < 3 The domain ofƒ¯is the interval [A, B]| where A = and B =

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Q: Write the differential equation and then determine whether you have overdamped,critically damped,or…

A: Introduction: The differential equation of motion of an unforced damped harmonic oscillation is…

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: , find: a. the domain and range of f in interval notation For f(x) = /x+17 1. 2 Ans la D, : R, b.…

A: Given: fx=x+172 for finding domain and range of given function, first we draw graph of it as below…

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A: A discontinuous graph of f' is given Both pieces of the function of the form of parabola. Assume…

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, ƒ'(1) = 1, g'(1) = 5. For the following…

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Q: 32. (Refer to the graph of f below) On which interval is f concave upward? y4 y= f(x) -2 6 x 8 -2…

A: The solution are next step