What is the average rate of change of the function f(t) = t² - 7t between t = and t = -4? -10 -14 -13 O-16

Q: Find the following Wronskian: W(4, 3t, e-³¹, te-³1) O-972e-6t 0-972e6t 6 972e6t O 972e-6t 00 O-6

A: We can find the Wronskian .

Q: 8. Use the graph of the function f to find the following: 13 (-5,0) 4 -3 -2 -1 (-3,-2) 3 2 H (-1,-2)…

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Q: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.

Q: (5x¹2xy)dx + (6y+kx²)dy = 0

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Q: (x³ − 2y²)dx + 2xydy = 0 -

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Q: 01. |x2 - 1\dx = a. b. 2 C. 432 - 23 23 d. 틀-

A: This question can be solved using the concept of definite integrals and modulus function.

Q: 3. (x² + y²)dx - 2xydy = 0 [Answer: x²-y² = cx]

A: Here we use the method of substitution y=vx then dydx=v+xdvdxsee below the calculation and…

Q: Part c: ( 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2.…

A: We have to find the gradient and directional derivative.

Q: Given the graph of f(x), the function is continuous from the left at x = -1. True or False? Select…

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Q: If the line y = 2 is the horizontal asymptote of the curve y = f(x), then /(2) is undefined. Select…

A: To find whether given statement is true or false.

Q: r(t) = (−2 cos (2t), 3 sin (3t), In (2t)), then the fr(t)dt is equal to 3 Cos cos 4 where C is a…

A: Given:    rt=-2cos2t,3sin3t,ln2t then  ∫rt dt =∫-2cos2t,3sin3t,ln2tdt…

Q: In Exercises 19-24, match the parametric equations with the paramet- ric curves labeled A through F.…

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Q: ) Consider a horizontal parabola of the form ay² +by+ c = x wherea #0 and whose graph contains the…

A: Given problem:- Consider a horizontal parabola of the form ay² +by+ c = x whose graph contains the…

Q: Let A = A(r) give the area of a circle of radius r. The instantaneous rate of change of the area as…

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Q: ind f. f ″(x) = −2 + 24x − 12x2,    f(0) = 2,    f ′(0) = 18

A: We can solve the given equation.

Q: P₁: -60x + 90y + 120z = 29 P₂: 4x - 6y - 8z = 5 P3: -20x + 30y + 40z = 4 P4: 12x18y + 24z = 9

A: Follow the procedure given below.

Q: Find the radius of convergence, R, of the series. 00 Σ ( + 9)" 97 In(n) n = 2 R = Find the interval,…

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Q: If p = (7, 2) q = (5, -1), find p - q.       a)  p - q = (2, 1)   b)  p- q = (12,1)   c)  p - q…

A: p = (7, 2) q = (5, -1), find p - q here we have to make substraction of set here we have to…

Q: Evaluate f dac x²-x+2

A: We can evaluate the integral as below.

Q: What is lim O -∞ 0 1 2 O +∞ x^x + x^ I 2-700x + √x-2x√x²

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Q: Find dy dr dy dr for y = ㅇ 2 5+ 6t dt.

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

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Q: Evaluate fx and fy at the given point. (If an answer is undefined, enter NONE.) f(x, y) = cos−1(xy),…

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Q: Let f(x)= 4x²-19x-5 x² +11x-80 (A) lim f(x) X-5 Find the indicated quantities, if they exist. (B)…

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Q: Find the derivative of the vector function, r(t) =

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Q: Let f(x,y)=- lim f(x,y)? (3) (4.4) lim (x,y)→(4,4) This option Which of the following is true about…

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Q: Given the graph below, what is the lim f(x)? x-1+ +8 02 1 -10 -5 does not exist 10 -5- -5- -10 10

A: Using the concept of right hand limit

Q: Find the smallest number of terms of the series Σ1 partial sum sn is within of the sum. 1 100…

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Q: Present a second order differential equation. Identify the corresponding auxiliary equation.…

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Q: - 2. (x²y² + xy + 1)ydx + (x²y² − xy +1)x dy = 0

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: Question 17 sin Given: f(x) = {¹, if x #0 2T if x = 0 What should be the value of k so that f is…

A:

Q: Every student who wishes to enter the public library at Hotel de Ville (HdV), in the center of…

A: The solution is given below

Q: What is the slope of the tangent line to the graph of x^2 - xy + 3y^2 -2x + 4y = 17 at (5,1)

A: We have to find the slope of the tangent line to the graph of x2 - xy + 3y2 - 2x + 4y = 17 at (5, 1)…

Q: Evaluate et +2e2t-et e2t +1 dt.

A: Given that a integration problem and we solve this problem by using general property of integration.…

Q: Use logarithmic differentiation to find dy dx · if y = x¹(1+x), x > 0.

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Q: Which of the following rational functions is equivalent to the partial fraction decomposition 2x 2x…

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Q: How did you found x and dx? I 'm lost in that part

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Q: Find f tan 0 de. ] a. C. - In sin 0+ C - In cos 0+ C sec² 0 + C - In sec 0 + C

A: Here we have to solve the integral.

Q: Use Leibniz's rule to find dy dx dy dx for y= 8x-1 √ (t4-5) dt.

A: Concept: Newton Leibniz Theorem : Newton Leibniz A formula for differentiating a definite integral…

Q: Let f(x) = 2x+1, if x1 O (-∞, 1) U (1,00) O (-∞0, 1] U (1, ∞0) OR O (-∞0, 1) U [1,00)

A: topic- limits and continuity

Q: = √ Evaluate 1 /x(1 + √x)² dx.

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Q: A B O A OB D 1 4 1 4 f sec² (4t) (3 tan(4t))³ dt 1 16 (3 tan (4t))+ + C (3 - tan (4t))+ + C E None…

A: This question can be solved using the concept of integration by substitution.

Q: Which of the following is a valid expression for cos ¹ x? 04-sin-¹ a 01/2+ + sec¹ a 1 sec-1 01-…

A: The given expression is cos-1(x)We have to find the valid expression for cos-1(x)

Q: π sin" g 2. So cos² g dg

A: The given integral is;  Sin5g/Cos2g, limit from 0 to pi.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: with the initial condition y(1) = 4. -0 Y

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Q: r(t) = (-3√√9-1²,4 sin (4t), 2 In (-3-2t)), then the domain of r is given by the interval Select…

A: Here, r(t)=-39-t2, 4sin(4t), 2ln(-3-2t)

Q: To find a partial fraction decomposition, we should write: x+6 x²-11x+30 Select one: O True O False…

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Q: Work Problem You must provide a clear and detailed solution for the question. Let 2 = (y - 2x) ³,…

A: To find out the partial derivative.