*Introduction to Derivatives (x²+2x-3 if x#1 (4 Using the 3 conditions, show that f(x) = is both continuous %3D x-1 if x = 1 and differentiable at x = 1.

Q: I = Sin 52 ()

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Q: Question The graph of y =f(x) is shown below (dashed curve). Manipulate the green draggable points t...

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Q: 6.convergence set of the following power series: so (-1)". xn En=1 Ln=1' п. зп+1

A: The given power series is; Sum of (-1)nxn/[n.3n+1] , n from 1 to infinity.

Q: Consider the following. y = 3   (x − 4)2(x − 8)2 y = 0 x = 4 x = 8   Use the integration capabilit...

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Q: [4 51 [A] = |1 2 15 6] [4 3 7] [B] = |1 2 6 l2 0 4] Perform the following operations: 1. [E] + [B] 2...

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Q: х — 1 x² + 8x + 15

A: The given rational expression,                x-1x2+8x+15

Q: EXAMPLE 3 Find the area of the playing field described by R: - 2 s x S 2, - 1- V4 - x < y<1 + V4 - x...

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Q: A large tank filled with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon i...

A: Let A(t) is pounds of salt in the tank at time t.We know that dAdt=Rin-Rout

Q: Calculate y', y" and y" for y = . [Hint: y= r-le", product rule, several times.] use

A: Topic  - differentiation by parts 

Q: 4. J(2y + 3)? у+2 dy

A: Find your answer below 

Q: Solve the given differential equation. All solutions should be found. dy = e + 15y da NOTE: Use c fo...

A: Given:- y'=e9x +15y  To find:- General solution for given differential equation

Q: 1. A stone is thrown vertically upward from the top of a house 50 ft above the ground with an initia...

A: Due to Bartleby guidelines, only 3 sub parts can be solved. Please repost the remaining questions to...

Q: Find the derivative of the function. g(x) = In(x – 5.1x=1) g'(x) =

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Q: Give three points that are equivalent to the polar point ( – 8, 335°). Write the three points in pol...

A: Give three points that are equivalent to the polar point (-8 335°).

Q: 2. Determine whether the statement is true or false. [3, xs2] l0, x>2/, then lim f(x)=3. a. If f(x)=...

A: f(x)=3x≤20x&gt;2  

Q: dx ト メ

A: Method of substitution is used 

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

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Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact ...

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Q: Assume that 0 is an angle in standard position whose terminal side contains the point (-24,7). Find ...

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Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequence x2 + 1 An = ...

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Q: evaluate the given integral

A: The objective is to evaluate the integral.

Q: The integral of the given function | cos(9x) cos(5x)dx is equal .. 14 sin 4x + 4 sin 14x А. · + C 12...

A: This question can be solved by applying the formula of 2.cosA.cosB

Q: 3. Determine f(x) = x +x-2 is continuous on the given interval (-0,+0) (show graph and its table of ...

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Q: What is the angle of elevation of the sun when a 41-ft mast casts a 10 ft shadow?

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Q: 2 сos(6x) — 6 2? — 2 os(6x) – 6 x² sin(5x) – x2 – 5x - | lim x → 0 - -

A: We have to calculate the given limit: limx→02cos6x-6x2-2sin5x-x2-5x

Q: ctions of 0 by using the given information. cos 0= and sin 0<0 41 = (Type an integer or a fraction.)

A: Topic:- trigonometry ratios  

Q: 7.7.009. MY NOTES ASK YOU Find the fluid force on the vertical side of the tank, where the dimension...

A: Analyze the diagram

Q: n (2x-1)" n 4n n=1 1 Σ (r- 3)" n In n n=2

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Q: Evaluate the following improper integral. If it diverges, then type DNE. Otherwise, find its exact v...

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Q: )an = (-1)n-1" +10 sin(n) 3n + 2

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Q: Find the derivative of the given function at a given number. 1. y = 3x² - 2 at f'(1)

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Q: Solve, in terms of Bessel function, the DE: x²y" + 7xy' + (36x6 + +)y = 27 y = 0 4

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Q: 5. Verify that, for any constant C, y = t+4vt +C satisfies the differential equation (y-t)y' = y-t+8...

A: Given differential equation 

Q: sec Odo

A: ∫1tdt=lnt+C

Q: 7. Determine whether the sequence an = (-1)" is bounded. Determine whether the sequence is monotonic...

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Q: For the next five questions, consider the following differential equation: (y? + cy°)dx + (5y² – xy+...

A: Given differential equation is y2+xy3 dx + ( 5y2-xy+y3siny) dy =0 Also, given that M is coefficient ...

Q: A number of matrices are defined as [A] = |1 2 l5 6] [4 3 71 [B] = |1 2 6 l2 0 4] Perform the follow...

A: Note: Since you have posted a question with multiple sub-parts we will solve the first three subpart...

Q: x² – 21x + 54 - lim x → 3 х — 3 - II

A: x2-21x+54=x2-18x-3x+54=x(x-18)-3(x-18)=(x-18)(x-3)

Q: For the graph of the equation, identify the amplitude, period, phase shift, and vertical shift. Do n...

A: Given,            y=-4sinπx-1+5To find : The amplitude, period, phase shift and vertical shift

Q: Will the limit of all polynomial functions f (x) as x approaches a be always equal to the value of f...

A: To write that the limit of all polynomial functions f(x) as x approaches a always equal to f(a). 

Q: Identify and Sketch a) x= yea 4 2 2 b.) + 16

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Q: Find the solution of the given initial value problem. ty' + 3y = t – t+ 5, y(1) = 3, t > 0 y =

A: ty' +3y=t2-t+5  

Q: Find the function r that satisfies the given condition; r' (t) = i+ te-tj-4k;r(0) = i+ t2+1 - 3k

A: Given problem:-

Q: Solve the given differential equation. All solutions should be found. dy -2y NOTE: Use c for the con...

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Q: Find the arclength of y = 4x°/2 on 2 < x < 4

A: To find the arc length of the curves: y=4x42 on 2≤x≤4 Now, the arc length formula on a≤x≤b is given ...

Q: dx/y-xdy/y^2=0 solve using exact equations (diff eq)

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Q: aqu o sanb Using Formula i and solving for the required integral, we get j sec's de - {(see x tan x ...

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Q: In x Use the change of base formula loga x = to show that In a log, x = dx x In a d d loga x = dx dx...

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Q: Let f(x) = 2x3+3x2 - 12x +5. a). Find x values on the graph of f at which the tangent line is horizo...

A: This question is based finding slope of a function by using differentiation.

Q: de 1.

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