Discuss the continuity of the function. X 4 f(x) x + 2 = f is discontinuous at x = 1 1 -5 -4 -3 -2 -1 LO 5 4 3 2 1 -1 -3 -4 -5 1 2 3 4 Xx

Q: Use the properties of the derivative to find the following. ti + 4tj + t²k, u(t) 5ti + t²j + t³k (a)…

A: Note:As per bartleby gudlines we are supposed to answer only3 sub-parts (if there are multiple…

Q: 37. y = |x - 1| 38. y = |x + 1| For the following exercises, graph the given functions by hand. 40.…

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Q: 4. A vector with magnitude 10 points in a direction 27° clockwise from the negative r-axis. Sketch a…

A: The objective of this question is to sketch a vector and find its components. The vector has a…

Q: Find the volume of the solid that is generated when the region enclosed by the given curves is…

A: To find the volume of the solid that is generated when the region enclosed by the given curves is…

Q: 2. Find the total area between the region and the x-axis. a. y = -x²2x, -3 ≤x≤ 2 b. y = 3x²3,-2 ≤ x…

A: To find the area between the region and the -axis.

Q: Solve the differential equation. dy dx = 10ex-y Choose the correct answer below. O A. y = 10 In x +C…

A: Given Differential Equation is as follows

Q: In AABC, AB = 74 cm, CA = 85 cm, and A = 119º. A) What equation would you use to solve this problem?…

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Q: Consider the function f(t) = 4 sec²(t) - 10t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: The objective of this question is to find the antiderivative of the function f(t) = 4 sec^2(t) -…

Q: 3. If f(1)=10 and f'(x) ≥ 3 for all 1 ≤ x ≤ 5, how small can f(5) possible be?

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Q: Is the function shown continuous over the interval (- 5,5)? О Ay 5- 00 No Yes

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Q: Suppose that the​ cost, p, of shipping a​ 3-pound parcel depends on the distance​ shipped, x,…

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Q: The base of a solid is the region enclosed by thegraphs of y = , y = 2, and x = 0. For this…

A: The objective of this question is to find the volume of a solid whose base is the region enclosed by…

Q: ) f(x) (sin r)tan

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Q: Consider the following vectors. C = u = (8,5) V = Find a constant c for which u = cv. (If an answer…

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Q: Consider the following parametric equations for a line L₁. x = 6 - 3t, y = -4 + 4t, Z = 6 + 8t Find…

A: The objective of the question is to find the direction vectors for the lines L₁ and L₂, find the…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 3(1 − cos(t)) k t lim (t²i…

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Q: A tank contains 100 gal of fresh water. A solution containing 3 lb/gal of soluble lawn fertilizer…

A: Solution is following in explanation step.

Q: L-1 s+1 s² +2

A: To find

Q: Ex 4. Identify the symmetry, if any, in the following functions. Decide whether the following…

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Q: Consider the following plane. 4x - 2y + 3z = 6 Find the normal vector for this plane. n₁ = Find the…

A: The objective of the question is to find the normal vectors and specific points on two given planes,…

Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,

Q: Ex 5. A rectangle is constructed with its base on the x-axis and two of its vertices on the…

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Q: Q1) Estimate the area under the graph of f(x) = x² + 1 from x=1 to x=3 using four approximating…

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Q: 30. -5-4-3-2-1 y 5- 4- 32 -3- -5- 12345 V 31.

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Q: 8: A series n=1 an is defined by the equations a1 = :1, an+1 Determine whetheran converges or…

A: Given that The Ratio Test If  then series convegrent If  then series divergentIf  then result…

Q: 3. For f(x) = 2x + 1, find the value of f(x)-ƒ(3) and simplify as much as possible.

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Q: 16. How will you describe A set of data that are all close to each other, but they are not close to…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: need help explaining

A: The objective of the question is to identify the inequalities that correctly represent the interval…

Q: Describe the set S = {x: x² + 4x <5} as an interval. Hint: Plot x² + 4x - 5. (Use symbolic notation…

A: Set and intervals.

Q: Theorem: Recall the following theorems from algebra: Vr Ex 4. Graph the following functions i)…

A: The given functions

Q: Find the volume of the solid generated by revolving the region bounded by y = 2x², y = 0, and x = 4…

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Q: nd the lengths of the sides of the triangle ABC with the indicated vertices. A (8,-1,-1) B(6, 0, -8)…

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Q: Find all y-intercepts of the following function. Express your answer as a coordinate point in…

A: The function is given byTo determine: the y-intercepts of the function.

Q: Create a table of values for the function f(x) lim X-0 4 -0.1 -0.01 -0.001 Use the result to explain…

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Q: Now find the derivative of the function  y = ex6  using the chain rule.

A: The objective of this question is to find the derivative of the function y = e^(x^6) using the chain…

Q: Let f(x) be the following piece wise function f(x) = ( x ² + => if 0 1 Show lim f(x) does not exist…

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Q: Solve the given initial-value problem.(6y + 2t - 3) dt + (8y + 6t - 1) dy 0, y(-1) = 2

A: The objective of the question is to solve the given initial-value problem. The problem is a…

Q: 1. -1 y5-2y dy y² √2 s² + √5 s² 123² m. Si ds -8 (x¹/²+1)(2-x²/3) dx x1/3 n. Si 1

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Q: A rectangular piece of cardboard measuring 12 inches by 42 inches is to be made into a box with an…

A: rectangular piece of cardboard measuring 12 inches by 42 inches is to be made into a box with an…

Q: b) 125x+2 = c) 73x+1 = 5.x d) 2(5)* = 3x+1 1-5x

A: To solve the following equations.Note: Since, the student has posted a question with multiple…

Q: Find the coordinates of the midpoint of the line segment joining the points. (5, 2, 8), (1, 4, 0)…

A: The objective of this question is to find the midpoint of a line segment in three-dimensional space.…

Q: Use the graph of the function f shown to the right to find f(-3), f(-2), and f(-1). f(-3)= f(-2)=…

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Q: Evaluate the integrals in the following exercises using integration by parts. a) fxsin dx b) J0cos…

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Q: y+4 f) 1/2 2 dy +v

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 3. +y =p³x dy dx

A: According to the condition we can solve only one question.

Q: Find r(t) u(t). r(t). u(t) r(t) = (4 cos(t), 9 sin(t), t – 4), u(t) = (18 sin(t), −8 cos(t), t²) Is…

A: The objective of this question is to find the dot product of two vector-valued functions r(t) and…

Q: why is it not +C  for (ln(3)+ln(5))/2

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Q: Find the limits. f(x) = x + 5 g(x) = x² (a) (b) (c) lim_f(x) = = x → 5 lim_g(x) X→ 4 = lim_g(f(x))…

A: The objective of this question is to find the limits of the given functions as x approaches certain…

Q: The exponential models describe the population of the indicated country, A, in millions, t years…

A: The exponential models describe the population of the indicated country, , in millions,  years after…