4. Let L be the line segment L = [-i, 2i]. (a) Use the Triangle Inequality and the Reverse Triangle Inequality to show that for every z E L we have |z − 1 ≤3 and z+4|22.

Q: 1.52. Let M and N be nonnegative real numbers. Suppose that x + y ≤ M and |xy| ≤ N. Determine the…

A: Given: The inequalities x+y≤M and xy≤N. M and N are non-negative real numbers. To find: The maximum…

Q: Determine the x-values at which the graphs of f and g cross. If no such x-values exist, then state…

A: This question is related to Functions, we will solve it using given information.

Q: Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b. We define…

A: Given that: Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b.…

Q: Find the absolute minimum value of f on the interval [0, 4] when f(x) = 16x + x². 1. abs. min. value…

A:

Q: 05. What is the positive interval for y =l-3x - 6| + 2? A. (-∞, –2) B. (-2, +∞) C. (-∞, +∞) D.…

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Q: Let a and b be real numbers. (a) Prove that a| – 16| < la + b| and |b|- lal < la + b|. (b) Use part…

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Q: 3. The speed, in km/h, of a certain car t seconds after passing a police radar location is given by…

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Q: 6. Prove the following inequalities. (a) | sin(x) – sin(y)| 1

A: To prove the following inequalities. sinx−siny≤x−y for x,y∈R x−1x&lt;logx&lt;x−1 for x&gt;1

Q: O x = 4 ve Find all points where the function is discontinuous. e

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Q: For what Values of "" does the function Satısfy the differentiel equetion y"-By + Zy=0

A: Given equation is : y=erx To find the value of r for which satisfy the differential equation…

Q: 12. The path of a soccer ball is modelled by the relation h = -(d – 28)² + 49, 16 where d is the…

A: As per the guidelines, we are suppose to answer only 1st 3 parts..I have provided answer for the 1st…

Q: Let fx) = 3-402-11x. Use a sign analysis to find a) on which intervals is f concave up ? concave…

A: We need some basic definition here like concave up, conacave down, inflection points. So let's…

Q: 5. (a) Find the values of X₁ and x₂ in the figure. (b) Find the largest positive number & such that:…

A: see below the answer and explanation

Q: 12. The functionf is defined on the interval [-2, 3] by f(x) = (3+2x - x2)'. If M is the maximum…

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Q: need help

A: If you have any questions let me know in comment box thankyou for your question.

Q: 2. Find the exact length of the curve y = 16 2x² on the interval 2 ≤ x ≤ 3.

A: The given curve is:.To Do: Find the exact length of the curve on the interval .

Q: Select all of the graphs in which the intermediate value theorem would apply for the interval [1,5].…

A: For Intermediate Value Theorem the function should be continuous in the closed interval.  For our…

Q: (a) By drawing a suitable diagram, prove the triangle inequality |z1 – 2| > |21| – |2|-

A: