Prove that if 0 < a < 1 and b = 1-√1-a, then 0 < b < a.

Q: secy, (0)

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A: a) Find an equation of the line tangent to the graph of y = x2 + 1 at the point (2, 5)b) Find an…

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A: Given function is We have to find the interval of continuity.

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A: To calculate the limit of the function.

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Q: Consider the function below: 64 T (-1,4) (-1.9,3.0) -3 -2 -1 0 -2- 2 3 4 (0.6,-1.2) 5 Is the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: To calculate the limit of the sequence.

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A: All the given limits have been marked except " e " . So we solve question "e" .

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Q: (3) (3) 5. Simplify f(x) = 3 + i (a) f(x) - g(x) and g(x) = -5 +i (b) f(x) • g(x)

A: Given Function are as follows

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Q: 4) If = y sin x and y = 2 whenx =, then y= A) e 2 cos.x C) e-cos x + 2 B) 2e cos. D) -cos x + 2

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A: The conditions to be function discontinuous at f(a) undefined Either undefined or undefined

Q: a) Find a function f so that f’(x) = 6x + cos(x). b) Find a function g with g’(x) = f’(x)

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Q: Determine an n so that the trapezoidal rule will approximate the integral 12 En = - 8 dx 6+x with an…

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Q: O a. f'(x) = (lnx + 6) [ln] x 5 O b. f'(x) = (tgx + 6) [tg) x 5 O c. f'(x) = (inx + 4) [In] $2x 7 O…

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Q: (d) lim 1-0 1 +3 - 3/1 I

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Q: Problem 7: Find an equation of the ellipse with foci at (−4,3) and (−4,−9) and whose major axis has…

A: Ellipse with foci at (-4,3) and (-4,-9) and whose major axis has length 30 .Let the equation of…

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A: Given function isWe have to find the absolute maximum and absolute minimum value of on We know…

Q: ery Check #1 ive Name: Ny Aisha Date: 1/31/24 2. Place the values of f(a), f'(a), and f" (a) in…

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A: That is;

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Q: 4. Sketch the graph of x3 - 4x² + 2x - 1 by labeling the maximum/minimum points, inflection point…

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A: By using polar coordinates to evaluate the following integral.

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A: Calculation for the critical points is as follows

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A: If  ​$700 is invested at interest rate​ i, compounded​ annually, in 3 yr it will grow to anamount A…

Q: -Suppose-Z₁ =3+2i, z₂ =4−5i . Calculate-|6z₁ - 9z₂|

A: AnswerGiven complex numbers z1=3+2i and  z2​=4−5i, we want to calculate the modulus of the…

Q: Let u = (2, -3, 4) and v = (-2, 1, 3). What is the dot product u v? What is the angle between u an v…

A: The given vectors  and