Find parametric equations of the line through (−2, 1, 3) that is parallel to 3i - 7j+k. x(t) = 5 t - 2 y(t) z(t) = -8t+1 = -2t+3 X X X

Q: x+2 find the absolute maximun and absolute minimur value of the following continuous function on the…

A: To find out the absolute maximum or minimum.

Q: Differentiate the following functions, giving your answer in a similar form, without negative or…

A: To differentiate the given function.

Q: 3. d dx Pick one by (and only one!) and prove it: [kf(x)]= = k f(x) d d.x d - [csc(x)]=-csc(x)…

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Q: A farmer is constructing three equally-sized pens against the side of a barn for his animals, as…

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Q: An island is 6 mi from the nearest point on a straight shoreline; that point is 12 mi from a power…

A: Concept: The slope of a function can be found in its first derivative. The slope of the curve grows…

Q: Write down the inequality involving p for which the integral S2² (x-25 da -2)² converges. For…

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Q: determine whether the sequence converges or diverges. if it converges, find the limit. (if the…

A: We can find whether the sequence is convergent or divergent .

Q: Evaluate Jc F. dr. F(x, y, z)=x² + y²j+z²k C: r(t) = 5 sin(t)i + 5 cos(t)j + Ostsn

A: Given: Fx,y,z=x2i+y2j+z2kC: rt=5 sin t i+ 5cost j+t22k   , 0≤t≤π.We need to evaluate ∫C F. dr

Q: An open rectangular box (no top) is formed with a square base and rectangular sides so that the…

A: Solution is given below:

Q: h(x)=-ln(x+2)

A:

Q: Write the sum using sigma notation: -1/8 + 1/10 - 1/12 + 1/14 - ... = Σ η= = 0

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Q: Find the limit using I' Mopital's Rule where appropiate. net, the some way ele several times). (IF…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: Fill in the spots in the integration process below based on the indefinite integral 4x²-25 S using…

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Q: 9. Consider the following 2 x 2 matrix A and basis S of R²: = [] and 5 = {[¹²₂] [²³₂]} The matrix A…

A: Given linear operator A=2456     and  basis   S= 1-2  ,3-7

Q: Find an equation of the plane with point P (2, -1, 3) and containing the line L: x-3 y+4 z-5 -6 10 =…

A: General equation of a plane passing through P(a,b,c) is, P(x-a)+Q(y-b)+R(z-c)=0....(i) Where P,Q,R…

Q: 13. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward the first…

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Q: 29. Convert a complex number in polar form shown below to a complex number in standard form (a +bi).…

A: At first we find value of cos 15 and sin 15 then we simplify the expression.

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

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Q: Find the linearization L(x) of f(x) at x = a. f(x)=√√6x4, a = 0 Select one: OA. L(x) = ² × - 2 OB.…

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Q: A. Find the orthogonal trajectory for the family of straight lines passing through the point (1,1).…

A: Concept: We differentiate the given family of curves with respect to x on both sides and get the…

Q: © 2r²y = y(y³ + 2x³) 02r³y y(y + 3x²) 1 y² = 2² a T

A:

Q: Find the indefinite below using the substitution x = tan (8). x √ √1² dx, for −1<x<1.

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Q: 34. Which function of the following is NOT continuous at x = 3 ? f(x) = X - 3 x2 + 5 f(x) = x - 3…

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Q: 4. At what point does the exponential function overtake the linear function on the interval (0,00)?…

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Q: -6 -5 -4 -3 -2 10 8 6 4 2 1/2 3 4 5 6 -2+ -4 -6 -8 -10 + The function graphed above is: Concave up…

A: A graph is said to be concave up if it is open up side and concave down if it is open downside. A…

Q: 5. Let f(x) = 2√x + 4. (b) (c) Find the domain and range of f. Graph f. Label at least 3 points on…

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Q: The function f(x) has a domain of (-∞, ∞) and a second derivative given by the following. F"(x) =…

A: Topic = Derivative

Q: PS #1 9. A ladder 10 ft long rests against a vertical wall. Let 0: angle between the top of the…

A: A ladder 10 ft long rests against a vertical wall.Let θ: angle between the top of the ladder and the…

Q: If the function y = e is vertically compressed by a factor of 8, reflected across the x-axis, and…

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Q: Given the function f(x) - A. Factor [Select] [Select] x(5x+5)(x-3) B. Find th x(5x+3)(x-5)…

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Q: 2x + 9 . For this function there are two important intervals: (-∞, A) Consider the function f(x) 3x…

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Q: 1. Find the length of the curve y = ln(secx), where 0 ≤ x ≤ (1.5 Marks)

A: Note: For a function f(x) and x=a to x=bthen arc length is given by ∫ab1+(f'(x))2dx. Now in the…

Q: Consider the following function, f(x), on the interval [-1, 8]. Absolute Maximum 1. Find the x value…

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Q: π Find the equation of the tangent line to the curve y = 2 sin x at the point The equation of this…

A: We can find the slope at the indicated point in the below steps.

Q: Find the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes…

A: The given function rx=3x2-30x+76x2-10x+25 We have to find the domain, range, horizontal and vertical…

Q: 4. Solve the given integral [(2x – xex")xdx 2x² In 2 2 4+² O C. In 2 - 3ex³ - ·+3ex³ +C + C e. None…

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Q: Use the Rational Root Theorem to determine the possible rational zeros for the function f(x) = 3x¹ +…

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Q: The domain of the function f(x) = √√e−4 – elx−3/−x is -4 е

A: domain of function fx=e-4-ex-3-x

Q: A piece of cardboard measuring 14 inches by 13 inches is formed into an open-top box by cutting…

A: Topic- Application of derivatives We are given, Apiece of cardboard of dimensions 14 inches by 13…

Q: 1) Aşağıdaki fonksiyonların Maclaurin Serisini bulunuz. a) f(x) = ln(x) b) f(x) = ln(x+1)

A: See the answer below

Q: In Exercises 5-8, sketch the graph of the given parametric equations by hand, making a table of…

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Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

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

Q: 1 for convergence, you 6k8 + 8k¹2 k = 1 will use the Limit Comparison Test, comparing it to the p 1…

A: soution:-∑k=1∞16k8+8k12ak=16k8+8k12Limit Comparison Test using the P series ∑k=1∞1 8kP where…

Q: In Exercises 39-42, write the equation of the hyperbola in standard form. 39. 3x - 4y² = 12

A: hyperbola is given that  3x2 -4y2 = 12 this is the question of the equation of geometry we have to…

Q: 3. Evaluate the determinant. 24 | a. 22 b.-12 c. -2 d.-18. e. -4

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

Q: Evaluate 112 (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 2

A: To evaluate the given line integral

Q: 1. Evaluate the given integral [(4x³ - 3√x)dx 3 12x² O a. 3 2√x O C. 2 3 1 x ² = ² x ² + c - C 3 + C…

A: Topic = Integration Correct option = b

Q: The graph of the derivative of f(x) is shown below: 7+ 6 5 4 3 2 -7 -6 -5 #4 -3 -2 -1 -1 -2 -3 -4 -5…

A: Topic = Functions

Q: A peach grower finds that if he plants 70 trees per acre, each tree will yield 80 bushels of…

A: Let x be the number of trees.

Q: Consider the function f(x) = 5(x - 2)2/3. For this function there are two important intervals: (-∞,…

A: As nothing is mentioned, we will be answering by the method of the graph. Thus, the critical number…