5. u = 2i, v = -3j

Q: Given f(x) = r³ – 2x2 – x + 2 on [1,2]. Verify the three conditions of the hypothesis of Rolle's…

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Q: ||P(t) × r"(t)|| Use the formula «(t) to find x(t). r(t) = t²i + t³j K(t):

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Q: Solve the differential equations: (a) = 4x+2x+5 where V(1) = 10 .

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: What are the slopes of the asymptotes for the hyperbola whose equation is 4x2-9y? = 36? %3D

A: Here, the given equation of the hyperbola is: 4x2-9y2=36 In standard from it can be written as:…

Q: 19. Using the l'Hospital's rule to find the limits e3r – 1 In(ln æ) 1 e" – 1- x – ² (a) lim a→0 In(x…

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Q: 486 on the interval [8, 20]. Find the absolute extrema for the function on the given interval.…

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Q: A small home business creates muffins, bones, and cookies for dogs. In addition to other…

A: Here, from the given data, let x be the number if muffins, y be the number if bones and z be the…

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 7 sin(x). If f(0) = 2 and f'(0)…

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Q: In spherical coordinates equation for the paraboloid z = 2 - x - y? is p(cos o - psin² ¢) = 2 |

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Q: Evaluate the integral sec² x tan? x + sec x (sec² x + 1) dx 2 sec x tan x (sec2 x + 1)

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Q: 21. A group of 10 women and 6 men must select a four-person committee. How many committees are…

A: Let's find.

Q: 5. Determine the values of x for which the function is continuous. 3r +1 e. f(x)= /x – 3 2- 8 4x d.…

A: The function √(x-a) is continuous iff x>=a The function 1/(x-a) is continuous iff x≠a

Q: Evaluate the integral (Partial Fraction Decomposition) xdx (x² + 2)(x² + 1)²

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Q: 3. 1 1 2 4 1 To find the blue shaded area above, we would calculate: | f(x)dx area а Where: a = b :…

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Q: Find an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and (−1, 2, 3). Show all…

A: Here we have to obtain an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and…

Q: Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

A: Topic = Vector

Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) 2x4 + 30x3 lim x→+o…

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Q: 5. Evaluate the expression without using a calculator. Show all steps. (a) sin (4) (b) cot(-210°)…

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Q: 4. Find the integral of your answer in problems 2a and 2b. CO

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Q: 6y² -dA where D is the region in the 1st quadrant bounded by y =x' and y= 4x . Evaluate 9.

A: Here we have to evaluate the  integral of a function over a region.

Q: L 4e3-1 dr = 7.96 x 10 True O False

A: To determine whether the given statement is true or false.

Q: Find y' if y= 2x + Vx*-9xr+3.

A: We can find y' in the following steps.

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: 7. 1. A = 4 6. 4…

A: 1.A=7-346 det(A)=7×6-(-3)×4=42+12=54 2.B=4-5-19 det(B)=4×9-(-5)×(-1)=36-5=31 3.C=213-312-27…

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y®)Zdy

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Q: Using a trigonometric substitution, the integral dz becomes: 2+25 (a) 25 (tan 0) (sec 0) de (b) 5 /…

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Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Here to of the function is at point (1,5), On left side function is increasing ,and at right side…

Q: Evaluate the integral (Partial Fraction Decompo! X + 4 J (x2 + 2)(x² + 1):

A: Evaluate indefinite integral.

Q: .4 dx (x² + 9)2

A: To evaluate the following integral.∫x4 dxx2+92

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: Find the general indefinite integral. (Use C for the constant of integration.) | (x2 + 2x - 3) dx…

A: The objective of the question is evaluate the indefinite and definite integral.

Q: The probability density function for a continuous random variable X has the form, Find the…

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Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0<t< 2n L =

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Q: A particle is moving with acceleration = 6t + 12. its position at time t = 0 is a(t) s(0) = 5 and…

A: First use the integration to find the velocity then again integrate to get the position function.

Q: Find the nine roots of -256 – j256/3.

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Q: x² – 2x – 1 dx (x – 1)2(x² + 1)

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Q: Question 1: Using appropriate substitution tan'x xp: sec5x

A: LetI=∫tan3xsec5xdxI=∫sin3xcos3(x)1cos5xdxI=∫sin3xcos3(x)×cos5xdxI=∫sin3xcos2xdxI=∫sin2xsinxcos2xdxI=…

Q: (2x + 6)dx x2 – 2x + 17

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Q: Arc Length With Vector Functions For problems 1 & 2 determine the length of the vector function on…

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +7 1 (?, ?) lim t+\6t2 + 7'5t

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Q: Calculate the volume generated by rotating the region bounded by the following curves about each…

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Q: x + 4 dx (x² + 2)(x² + 1)2

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Q: Directions: Prove the following statements. 1. If f(x) = (x² – 1)3 then f'(x) = 6x3 – 12x + 6x.

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Q: A firm estimates that it will sell N units of a product after spending x dollars on advertising,…

A: Given problems:- a) A firm estimates that it will sell N units of a product after spending x on…

Q: | 3t³ (t² + 4)5dt

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Q: A ball is thrown vertically upward from a point 112 ft above the ground with an initial velocity of…

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Q: e sin. *(sin x + cos x) dx ecos x

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y®)Zdy

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Q: 6. Given i [2, – 5]and i [- 7,2] find %3D а. 5 - b. i C.

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Q: The graph of f is given. Use the graph to compute the quantities asked for. (If an answer does not…

A: Above asked questions are given below.

Q: Only pose the triple integral that calculates the volume of the solid bounded by the surface y2…

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