Consider the following sequence: S 7" {an} = 1=1 An+1 to show that the given sequence {an} is strictly increasing or strictly decreasing. An Use the ratio Sequence is strictly increasing eTextbook and N decreasing

Q: 1. d'y_dy - 42 + y =r²-2t +3 dr dt 2. y"-7y'=(2x-1)sin 2x 3. y'-5y=xe" – xe*

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Q: Evaluate: x²-x+1 dx A 3 2 D 5 3

A: SOLUTION-

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Q: 2 integrate by parts

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Q: Classify the differential equation: h_p +sec x V dæ4 O Fourth order, third degree, linear ordinary d...

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Q: 2x + 2 x +1 in of Xト! ナイ

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Q: In order to evaluate the integral expression / In( sin(x) ) dv using simple substitution, dv=f(x)dx_...

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Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

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Q: etermine each function's domain and range. If applicable, use a graphing utility to confirm the hand...

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Q: O-26429052 2n (41) +1+(+り

A: We will use log function to evaluate the values of n.

Q: Using the substitution y = vx and dy = v dx+ x dv, the differential equation with homogeneous coeffi...

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Q: patient is adminstered a dose of 60 mg of a drug. If the body naturally disposes of 7​% of the dru...

A: Given query is to find the rate of change after 6 hours.

Q: Q3/ find the derivative La)= メ 2. logs (x+3) 2x+4

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Q: The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), an...

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Q: 12. e-v dy

A: Integrate e-√y w.r.t. y from 0 to infinity. 

Q: Question 21 Evaluate: J(3x + 1) d. S(3x+1)°d_

A: ∫3x+12dx

Q: A. FUNCTIONS 2 Given f(x) = 3x – 2 and g(x) =+, find each of the following: 3 (a) (f o g) (x) (b) (g...

A: If f(x) and g(x) are real valued functions then  (fog)=(fog)(x)          =f(g(x)) (gof)=(gof)(x)    ...

Q: F. Planes and Lines O Find an equatin The plane each of whose paints idistant to The agu w eq point ...

A: Here ,              We have given two points which are               equidistant from each points of...

Q: Vミ-2 lim ミー→4 -4

A: Let, L=limz→ 4z-2z-4Rationalize Numerator L=limz→ 4z-2z-4z+2z+2 L=limz→ 4z-4(z-4)(z+2)L=limz→ 41(z+2...

Q: 4 x2 + 4

A: We have to find out the antiderivative

Q: Write the first five terms of the sequence: +oo {Vn² + 7n – n}n=1 - Determine whether the sequence c...

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Q: tan3x)dx tan Evaluate: cos23x A - In|sec (tan3x)|+C - In|cos (tan3x)| +C B © In cos(tan3x)| +C in se...

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Q: E. DIFFERENTIATION Obtain the derivative of the following functions: (2x³-1)5 y = (5-3x)*

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Q: y = 5t2 - 2t + 4 -'(t) =

A: Given query is to find the derivative of the expression.

Q: Which of the following indefinite integrals will result to logarithmic expression? 2 (2x +7)2 B None...

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Q: 9. DETAILS SCALCET8 8.2.027. If the region R = {(x, y) | x 2 1, 0 s y s 1/x} is rotated about the x-...

A: Given :f(x)=1x=y ∀x∈[1,∞)To find volume of the given region :V=π∫aby2dx  

Q: 2 y = | (x 3. 4x + 5) dx

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Q: 2. y = 3x - 8x3 + 6x2

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Q: Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x) =...

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Q: Find the volume of the solid generated by revolving about x=0 the region bounded by the given lines ...

A: Solve by volume revolution

Q: Which of the following integration expression can be transformed into integral of power 2 dx (A) 1+4...

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Q: / tan( 4x + 3) dx Evaluate: (A) –In |cos (4x+ 3)|+C 4 B 4 ® -im [sin(4r + 3)| +C В –In |csc (4x+3)|+...

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Q: VI. Show that ydx = y dx it must be (a <h<b)if f(x) = 2x, a = 1, h 2 and b %3D = 4 20. f(x)dx is equ...

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Q: 3x3-5xe* +2xcos(x) Evaluate: dx A x3 - 5e* – 2sin(x) + C 3x4 B 5e* +2sin(x) + C 4 © x3 - 5e" + 2sin(...

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Q: a | sin(Inx)dx =x[asin(lnx) + dcos(Inx)] + C Find: a + B + 8

A: Here, to evaluate: I=∫sin (ln x) dx...(1)  

Q: Express the solution of the given initial value problem in terms of convolutional integral. A. y" + ...

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Q: Evaluate the integral: cose de. 4- sin?e ® sn- (ane) + c A sin-1 B -sin- sin- + C (c) -sin-1 sine+ C...

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Q: 9. An employee borrows Php60,000 for seven months at an interest rate of 12% per year. Find the inte...

A: Principal=P=Php60,000 Rate=r=12% per year Time=t=7 months=712 years Interest=Int=P×r×t100=60000×12×7...

Q: - (sin(Inx?))² Which of the following is equivalent to the integrand of | dx? A None of the given ch...

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Q: X x²dx 5+ x2

A: Find the integral

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A: This is a question related to mathematical logic. Based on the tree diagram we will solve the questi...

Q: If two functions F & G are both antiderivatives of the function f , the F (x) =G(x). (A) True B Fals...

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Q: Jack buys calculators for $6.00 each, envelopes for $.50 each and pens for $1.50 each. He spends a t...

A: Jack buys calculators for $6.00 each, envelopes for $.50 each and pens for $1.50 each. He spends a t...

Q: In the integral, cos?tsin2tat , the correct u using general power formula is; A sint B sin?t C) None...

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Q: dx 4+e¬*

A: Since we are given with the multiple number of question and our guideline is solve first question on...

Q: xdx 5+ x 2 X

A: Here,             We have given an indefinite integral                now we have to solve this and ...

Q: [sin(Inx?) ]²dx Which of the following is equivalent to :? sin(Inx14) dx A sin2( Inx 14) dx ® / B si...

A: ∫sinlnx7 2dxx

Q: The graphs of the functions f and g are shown in the figure. y 4 f 1 -1 1 2 3 4 6. f(x) Let u(x) = f...

A: topic - functions and derivatives