Q7 Given f(x) = 5-6x² + x³. How many critical numbers could f(x) have? (a) 0 (b) 1 (c) 2 (d) 3

Q: 6. a) Determine the slope of the tangent to the curve (shown in the picture) at the point whose…

A: Given curve is g(x) = 5x.

Q: Given f(10) 50 and f'(10) Approximate the following values f(11) ~ f(9.5) a f(10.25)~ = = 2

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Q: If f(x) = √√2x + 5, find ƒ'(x) using Chain Rule ƒ'(x)= Find f'(5). ƒ'(5)=

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Q: Problem 3. Find the arc length of the semicircle y-√√9-x from (√5, 2) clockwise to (√5,2). (cf. page…

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Q: Which of the following represents the area interior to both r = 5-5 sin(0) and r = 5 sin a) 102 (…

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Q: If ƒ(x) ƒ'(x) = - 53 x - 7' what's f'(x)?

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Q: Find the arc length of the curve below on the given interval. 3 5+² 4x y = 3 on [1,4]

A: The curve is y=x33+14x and the interval is 1,4.To find: Find the arc length of the curve…

Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: (a) Sketch y = secx on a restricted domain of length 7 where the function is one-to- one. Choose…

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Q: Find the derivative of the function. y = x²ex - 2xex + 5ex y' = x² et + 3et 2

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Q: Sketch the given plane vector field and determine its field lines. F(x,y)=xi-yj Which of the…

A: We have to find the vector filed of the f

Q: 1. Use the definition of fy = limo f(x,y+h)-f(x, y) h to find fy for f(x,y) = 2y²x³ + y

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Q: Name the line of symmetry as polar axis or 0= or neither. a. r=2cose b. r=2csc0 c. r = 3+5 sec 0 d.…

A: For θ = π2 symmetry,Replacing (r, θ) with (-r, -θ) gives the same result.Similarly,For polar axis…

Q: ng circle. Then, write the equation of the circle in both Standard -8 -6 y 6 + 4 24 -4-20 -6+ -8+ N…

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Q: A particle moves with a velocity of v(t) ft/s along an s-axis. Find the displacement and the…

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Q: H/F.. F. dr, where C is given by the vector function r(t) Evaluate the line integral F(x, y, z) = (x…

A: line integral

Q: 2-x Find the domain of f(x) = x2+18x-40

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Q: An open-top rectangular box is being constructed to hold a volume of 300 in³. The base of the box is…

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Q: A box is being constructed with a rectangular base. The base has length 3 times its width. If the…

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Q: Prove that if (c, f(c)) is a point of inflection of the graph of f and f" exists in an open interval…

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Q: Find the function f(x). 15 COS(EZ) 3 r5 * ƒ(x) dx = [In(x) · cos

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Q: Consider the following. f(x) = x2/3, Xo = 1 (a) Find the linear approximation L(x) to fat xo. L(x) =…

A: The linearization or Linear approximation of a function f(x) at the point x0 is given by…

Q: Find for y=x cott²dt. dy dx 2

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Q: Use implicit differentiation to find y² + 3x³ dy dx = = 4y - 2x² dy dx

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Q: Evaluate the double integral by first identifying it as the volume of a solid. J√₁5 5 dA, R = {(x,…

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Q: Evaluate the following integral. Sxxdx x-8 X √₁₂dx=+c x-8 (Type an exact answer.) +C

A: We have to slove above integral

Q: A ball is shot straight up into the air with initial velocity of 44 ft/sec. Assuming that the air…

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Q: 5 If sin(x) = - and is in quadrant I, determine the exact value of each of the following. Use 8…

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Q: A solid occupies the space above the region in the plane described by inequalities: 3 ≤ x² + y² ≤…

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Q: Find all solutions of the equation. to the nearest thousandth. SEE EX 29. log_(2)(4x+5)=log_(2)x^(2)

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Q: Evaluate the following definite integral. Express your answer in terms of logarithms. dx 2 1…

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Q: Calculate double integral in cartesian coordinates with steps. Double integral attached as image.…

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Q: Find the work done by F= (x² + y)i + (y² + x)j + ze²k over the following paths from (5,0,0) to…

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Q: A model for the surface area of some solid object is given by S = 0.253w0.9020.461, where w is the…

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Q: The terminal side of angle θ intersects the unit circle in the first quadrant at (6/11,y). What are…

A: The terminal side of angle θ intersects the unit circle in the first quadrant at 611, y. To find the…

Q: 32 Determine the maximum and minimum values of the function f(x) = 2x+² on the interval -2≤x≤8.

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Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

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Q: Question 19 Suppose that f is continuous on [1,5] and f(x) ≤ 0 if and only if 2 ≤ x ≤ 3. If 3…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 8t,…

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Q: Taking into account identical letters, how many ways are there to arrange the word PARVAMONSTRA that…

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

Q: Show that y = 2³+3x+2satisfies the differential equation " + xy" - 2y = 0.

A: Explanation:-

Q: Let J = 31 +43 - K and ✓ = 2₁ +3₁-2k be of two vectors. Find the component and projection U in the…

A: u→=3i+4j-k,v→=2i+3j-2k

Q: 15. on the interval (012), the function y = x³ + 3x2 - 4x +27 has an absolute max when X= A. 2 В. О…

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Q: 16 Find the area of the region bounded by the curve y=- 2 x-2x-63 The area of the region is (Type an…

A: y=16x2-2x-63 Graph:-

Q: E-76 =(7)5 71 (7) £75-3

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Q: Find the derivative of the function. h(x) = x² arctan(9x) h'(x) =

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Q: 3 Use the definition of the definite integral to evaluate (5x+1) dx. Use right Riemann sums and…

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Q: Evaluate [₁x (x + y)ds where C is the straight-line segment x = t, y = (2-t), z = 0 from (0,2,0) to…

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Q: 1 In a parallel electrical circuit the impedance Z can be calculated using the equation Z= 1 Z1 Z2…

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Q: use a test of convergence to determine if the follow series converges or diverges: summation where…

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