Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an ans f(x) = In x, 0 < x < 3 absolute maximum value .693147 local maximum value absolute minimum value local minimum value

Q: 5. Use the definition of the Taylor Series to find the Taylor Series for the function f(a) 2- cos(x)...

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Q: Evaluate the integral x Inx dx Select one: Inz -+C Oi In r- a +c 0 in z- +c 3. a Ina O None of them ...

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Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the x-...

A: Given: y=3x3 for 0≤x≤1

Q: True or False: If 3 dx%In|x-3|+B In|x+2|+C (x-3)(x+2) 2 then B =

A: true find integration use partial fraction  

Q: d: (a) lim ズー2 オー2--(*+1)

A: Answer:  The solution is as shown below:

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Q: he given series converges or diverges. use the following as proof: rison Test, Integral Test, Series...

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Q: Transformation by Trigonometric Identities Evaluate: integral of sin^12 2x cos^7 2x dx. Use the guid...

A: Let I is the value of Integration.

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Q: Find lak| for the series. 00 k k k + 12 k=0 (Express numbers in exact form. Use symbolic notation an...

A: The series ∑k=0∞kk+12k

Q: Ihe Water Level Was 6m at belining-QFindthe IWater Levet a any Zime QFind the 2ime when the tank emp...

A: This question can be solved by applying the equation of continuity and integration.

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Q: 7. The current population of St. Catharines is about 133000. Suppose a major devel- opment is planne...

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Q: Find the area bounded by the x- axis and the graph of the function f (x) = 4x² + 8x +1,0 <x 3. (4 II...

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Q: 3. Solve for x: (3)*+1 = V3

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 1 x-intercep...

A: Given query is to find the rational function with given characteristics.

Q: Use L'Hopitals's rule to find lim (2 – x)tan(ra/2). (Tx x→1

A: We use elogu=u and l- hospital rules in this question to find limit.

Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate t...

A: To check the convergence of the given series.

Q: Carbon decays exponentially. How many grams of the carbon will be left in 139 years, if 123 grams we...

A: Initial amount P0=123 grams time t=96 years Amount left after 96 years =P=66 grams Exponential decay...

Q: Consider the function f(r) %3D f(1) has two inflection points at x = C and x D with C <D where C is ...

A: Given problem:-

Q: If a rock is dropped from a height of 249 ft, its poistion t seconds after it is dropped until it hi...

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Q: Use the First Derivative Test to find relative (local) maximum points, if any, of the given function...

A: a) y=x3-xDifferentiatey'=3x2-1For local max or miny'=03x2-1=0x2=13x=±13x=-13,13Substitute x=-13 in y...

Q: Using integration by parts and taking a > 0, the integral x In(ax)dx is equal to: In a 2 In(2a) - 3 ...

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Q: Evaluate the limit. 2x5–16x² lim→2 2.2+ a³

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Q: d²y x+2 for y=- X-3 8. Find dx2

A: Differentiate with respect to x. 

Q: Find the absolute maximum and minimum of f(x,y)= 4xy^2 - (x^2)(y^2) - xy^3 on the closed triangular ...

A: f(x,y)=4xy2-x2y2-xy3fx=4y2-2xy2-y3fx=04y2-2xy2-y3=04-2x-y=0 ...(1)fy=8xy-2x2y-3xy2fy=08xy-2x2y-3xy2=...

Q: Determine whether the series converges, and if so, find its sum. E-1(-1)k-1 6k-1

A: topic -  series convergence and divergence 

Q: X 11. Find f (9(x)) and 9(f (x)) for the pair of functions. f (x) = a² + 1 g(x) = x – 10 f (g(x)) =x...

A: The given function is: fx=x2+1gx=x-10 To find the value of fgx and gfx

Q: A pendulum consists of a 3.5 kg stone swinging on a 4.1 m string of negligible mass. The stone has a...

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Q: Use the First Derivative Test to find relative (local) maximum points points, if any, of the given f...

A: given 

Q: A draining reservoir has the shape of an inverted right circular cone with a base radius of 30 m and...

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Q: Write the general antiderivative. (Use C for the constant of integration. Remember to use abs 1 3x d...

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Q: x2 - 3x - 10 s 0 ² - 10 s 0 O [5, 0) (-0∞, -2] or [5, ∞) O(-00, -2] O(-2, 5]

A: Topic = Inequality Correct Answer [-2,5]

Q: Convert polar equation r=cos3 θ to cartesian equation

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Q: 1. Consider the curve of the function f (x) = 2x² a. Find an expression for the slope of the curve a...

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Q: Write an equation for the polynomial graphed below 6+ 5- 4 3- 2- 1- 4 1 -1- 2 3 4 -5 -3 -2 |-2- 3 - ...

A: Find your answer below 

Q: True or False: To evaluate the integral dz, 9. we use substitution withr= 3 sec 0, where Select one:...

A: Option B

Q: 2. Find the vertical asymptote/s of 7.x f(r) : %3D x2 - 3r- 28'

A: Here we have to find the vertical asymptote of the function f(x)=7xx2-3x-28

Q: 10x + 1800 The average cost for a company to produce x units of a product is given by the function A...

A: Given: Average cost for a company to produce x units of a product is given by a function A(x) =( 10x...

Q: Consider the function f(x) 2x + 6x2 18x 54. a. Find the first derivative. f'(x) b. List any critical...

A: Given problem:- Consider the function f(x) = 2x³ + 6x² -18x-54   a. Find the first derivative. f'(x)...

Q: 5. Water is pumped out of a horizontal cylinder through an opening at the top. Find the work (in jou...

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Q: What is the particular solution to the differential equation = (x³ – 1)(2 – y) dx with the initial c...

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Q: 10. x= cost; y = sin't

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Q: Use the First Derivative Test to find relative (local) maximum points or minimum points, if any, of ...

A: Given problem:- Use the First Derivative Test to find relative (local) maximum points or minimum poi...

Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal...

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Q: Find the specific solution to the following 2nd order non- homogeneous differential equation d2y/dx2...

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Q: use second derivaictive to find derivaitve 1 Crihalralues -3 and I (-a3) V(I, I'ntervals ofinerease ...

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Q: In the expression 5 +2 tan(30 + ) = 3 where 0 < 0 < a, then 0 in radians will be i. 36 17z ii. 36 29

A: topic - Inverse trigonometric functions

Q: You invest some money in the stock market at time t = 0 months. If f(t), measured in dollars per mon...

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Q: Tunorial ExSICISS And any Intercepts. 49x Step 1 To And the y-Intercepts, letx be zero and solve for...

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