DIRECTION: Solve the following problems in neat and orderly

Q: For the next three questions, consider the differential equation: y" - 2y + y = e arctan r 48. If th...

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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: 3x²-2x+1) **1) dx x+2

A: Topic:- integration

Q: Directions: Please write your solution on the space provided and boxed your final answer. *Introduct...

A: Topic-  continuity and differentiability 

Q: Find dy/dx by implicit differentiation. 7e^x^2*y = x+y

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Q: Qi) Let ū =2 5 , and w=-5 ニ|+ フ find Scalars and b such that a ū - aū t bū

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Q: In a certain city with predictable weather, the temperature (in °F) t hours after 8 am can be modele...

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Q: haracteristic. 40 80 160 (A) y 2.2 2.2 2.2 2.2 -8 -4 8. (B) y 51 62 73 95 -4 -3 (C) y 18 4.5 -2.2 3 ...

A: Topic:- function

Q: Consider the function f(x) = 8x + 6x1. For this function there are four important intervals: (- 00, ...

A: In order to get the critical points of the function we need to differentiate the f(x) and equate to ...

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

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Q: What is the coefficient of the term contaning the variable h when f(x +h) – f(x) is performed, and i...

A: Here we have to determine the coefficient of the term containing the variable h when f(x+h)-f(x)h is...

Q: 4) Let P be the pyramid with height h and square base of length 6. Use integration to find the volum...

A: Solution: The height of pyramid =h The length of square base =b 

Q: メ

A: Put √x=t then solve it. 

Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse 25 = 1 (...

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Q: 8. f(x)=3csc(x-x) f(x) Amplitude Period Vertical Shift: Horizontal Shift

A: Solution is here

Q: QUESTION 19 Define a relation S from R to R by (x, y) ES, if and only if x² + 3y² = 25 %3D (a) List ...

A: A function is a relation which describe that there should be only one output for each input. Or we c...

Q: 2. y' = 4x(2y3 -y)

A: Given differential equation, y'=4x(2y-3-y)..........(i)⇒y'+4xy=8xy-3⇒y3y'+4xy4=8x...........(ii)

Q: 24 Determine the values of the trigonometric functions of 0, where cos 0 = and tan 0 = 25 7 sin 0 = ...

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Q: Jse l'Hospital's rule to find the limit. HINT [See Example 4. x + 1 lim x+0 e*

A: limx→∞x+1ex = ∞+1e∞                    = ∞∞                    = indetrminant form Apply l'hospital ...

Q: Consider the function f(æ) = x²e3". For this function there are three important intervals: (- 0, A],...

A: The given function is  f(x)= x2e3x  Find critical point and interval of increasing and decreasing. 

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

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Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) 1 and f(0) = -3 x-1 3. lim f(x) = –2, 4. lim f(x) = +∞, x-2...

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Q: 12. lim [(x 5) - 3x] isOHOAHOH 3OH2 UA a. lim (x 5) + lim 3x IROCORO b. lim (x- C. X-5- lim 3x X-a -...

A: 12)limx→a[(x-5)-3x] = limx→a(x-5)-limx→a3x13) limx→1x2-2x-3x-2=12-2.1-31-2limx→1x2-2x-3x-2=1-2-3-1li...

Q: a) fx°/4-25x² dx

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Q: f(x) = cot? 1 %3D tan-1

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Q: Problem #1 Find 4x-5x2 +s dx Problem #2 Calculate f'(t) if fle)=3t°csct Problem #3 d4x-x+3 Calculate...

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Q: tollo

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

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Q: Let r(x) = f(g(h(x))), where h(1) = 4, g(4) = 5, h'(1) = 5, g'(4) = 3, and f'(5) = 7. Find r'(1). r'...

A: To find out r'(1). 

Q: evaluate the given integral

A: The objective is to evaluate the integral.

Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of...

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of derivativedydx=limh→0f(x+h)-f(...

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: Graph The data a Then Tind madel t trigunome tric represent the trend Ove the data your made!

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Q: C.O d. 7. Evaluate the lim e. x-0 0M bobivo a. 0 8. The limit of x as x approaches to c is equal to ...

A: Topic:- calculus Note:- as per our guideline if more than one question uploaded than only one questi...

Q: In +1 dx

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Q: Q12. The amount of infected people S in thousands by a new flu variant depends on the time t in days...

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Q: dx 9. 10. (x -

A: As per the company guidelines we can solve first question. I hope that the given solution will help ...

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)

A: The objective is to verify the conclusion of clairaut's theorm.

Q: Find the Laplace transform of the following: f(t) = sin(5t) cos(5t)

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Q: uppose that you have deposited a certain amount of money in a bank that pays an terest rate of 2.5%,...

A: Topic:- algebra

Q: 12 Find the arc length of y = In(1 – a2) on 0 < æ < 19 No decimal entries. Find the exact value. L

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Q: Evaluate the indicated trigonometric function of 0, where 0 is an acute angle determined by an inver...

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Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 10y ; y3 = x ; y (gr...

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Q: Two sides of a triangle have lengths 12 m and 16 m. The angle between them is increasing at a rate o...

A: Topic:-  trigonometry ratios  

Q: Evaluate the integral dx et – e-x Note: Use an upper-case "C" for the constant of integration.

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Q: For the following expression indentify the correct form for partial fraction decomposition. x3 + x2 ...

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Q: ∫x/(1+x4) dx=?

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Q: A number of matrices are defined as [4 5] [A] = 1 2 L5 6] [4 3 71 [B] = |1 2 6 l2 0 4] Perform the f...

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Q: B. Evaluate each integral dz 1. z²+4z

A: Evaluate ∫dzz2+4z=?