a² +x – 6 + a |æ – 2| if x < 2 1. Let f(x) : 4 if r = 2 . Find the value of a and b such that lim f(x) exists. if r > 2 - 2| 2

Q: х3 + 2x2 + х 1. iim х->-1 2x2 —— х — 3 х3 + 2x? + 7х 2. lim X→-2 2х — 3 х3 + x2 + 4x 3. lim X→ー3 2x2

A: 1) limx→-1x3+2x2+x2x2-x-3Apply L-Hospital Rulelimx→-13x2+4x+14x-1=3(-1)2+4(-1)+14(-1)-1=3-4+1-4-1=-1...

Q: 6. A water tank is shaped like a cone with the apex point at the bottom, where the cone has radius 5...

A:

Q: Express the surface area of revolution for: x = (y^4/4) + 1/(8y^2), 1 ≤ y ≤ 2; x@axis ( Express ds= ...

A:

Q: Let f(x, y) = (x² +(G))°. Determine the directional derivative of f at the point (1 0) in the direct...

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Q: Assume that a is an angle in standard position whose terminal side contains the point (5, 12). Find ...

A:

Q: Let R be an equivalence relation on A - {a,b,c,d) such that a Rc and bRd How many distinct equivalen...

A:

Q: How many saddle points does the function f(x, y) 116 – 18r 66y + 9x + 11y? have? Answer: (Input 0 if...

A: Given problem:- How many saddle points does the function f(x, y) =116 - 18x - 66y + 9x2 + 11y2 have?...

Q: u - 1 Find dy/dx, given y : and u =Vx + 2. u* + 1

A: We can find the derivative as below.

Q: 12) In Problems 12 through 14, given [ xa ]'= a xa-1, where a is any real exponent. =(x-1) =. Find A...

A: According to bartleby guidelines I can only answer the first question only question (12). Please rep...

Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 - ...

A:

Q: Write the first five terms of the sequence: +00 11 ln n) n Determine whether the sequence converges,...

A: Given

Q: x+tan x 4. lim X→0 sin x

A:

Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: bxy + 2b°y²)(x dx + ydy)> xdy -ydx

A:

Q: sinh(2 In(c)) = (A) 를 + (B) c² – (C)를 높 2c 1 2c2 (D) c -! 1 (E) 0

A: Topic = Functions

Q: Differentiate...

A:

Q: 3\k-1 Determine whether the series E=1l-) 4 converges and if so, find its sum. 7/2 4/7 714 5/7

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

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Q: The general solution of the differential equation (x + y)°dx – (y² – 2xy – x²) dy = 0 is

A:

Q: (-1)"n For positive integer n, let a, = 3" (a) Determine whether the sequence {a„} is convergent. (b...

A:

Q: 3. Let P= and Q = . Find the values of a and b such that Pis parallel to Q.

A:

Q: Question 2 For positive integer n, let a, (-1)"n 3" (a) Determine whether the sequence {an} is conve...

A: Let &lt;an&gt; be a sequence such that an≠0 for all n∈ℕ and an+1an→l . If l&lt;1 ,then limn→∞ an=0.

Q: Assume cos(t) = - where <t <a. Compute the following %3D cos(-t) = sin(t) = sin(-t) =U sin(-t) + cos...

A: topic - trigonometric ratios sin(-x)=-sin(x) cos(-x)=cos(x) sin2(x)+cox2(x)=1

Q: (x'y-xy°)(xdy+ydx) 3. +dy = 2xdx

A:

Q: There is a jump discontinuity at x = 2 and ƒ(2) = 3 %3D

A: There is a jump discontinuity at x=2 and f(2)=3

Q: Evaluate the expression. 3 4 O A. -81 O B. 81 Ос. 81 1 O D. (-81)

A: We can find the answer as below in simplified form.

Q: 4dt 5t+ 2

A:

Q: A model for tumor growth is given by the Gompertz equation = a (In b – In V) V where a and b are pos...

A: Given:  A model for tumor growth is given by the Gompertz equation, dVdt=aln b-ln VV, where a and b ...

Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818...

A: Let x=0.904818181818... Multiply 1000 on both sides.

Q: 21-24 Find an equation of the tangent line to the curve at the given point. 21. y sin x + cos x. (0,...

A: we  have to find equation 

Q: Determine if the series converges or diverges. If the series converges give its value. 10 Σ 00 n=4 п...

A:

Q: c) h(p,g,0) = psin@cose ah sin@cos0 ; ah = pcos@cose answer: - %3D ah =-p sinøsin0 d) W(P,V,8,v.g)= ...

A:

Q: floor refinishing company charges $1.87 per square foot to strip and refinish a tile floor for up to...

A: (a) To find: The equation for the amount C they will charge to refinish a floor when x≤210 Given inf...

Q: Problem 4 Show that arcsinh(x) = sinh(x) = In (x+ V/x² +1). %3D int: Let y = sinh¬' (x). Then x = Iv...

A: Topic:-  trigonometry

Q: 16 Evaluate ex12 (x4 – 2x² + 1)²dx. 81

A:

Q: The distance, in feet, a moving object has traveled after t seconds is given by 3t/(4 + t). Find the...

A: We can find the required acceleration as below.

Q: If * = 2 tan(0), then a. cos(0) Vx2 + 2 Ob. cos(x) = Vx2 + 4 c. sin(8) = Vx2 +4 O d. cot(0) 2 е. sin...

A:

Q: Use the Simpson's Rule to approximate the given integral with n= 8. (Find Ss.) Round your answers to...

A:

Q: sinh? 2x dx 3sinh? 2xdx

A: Given ∫-3 sinh3(2x) dx ⇒∫-3 sinh3(2x) dx⇒-3∫sinh3(2x) dx Now solving ∫sinh3(2x) dx substitute u=2x→d...

Q: (у?- бу+1) dу y-3

A: ∫un du=un+1n+1+C

Q: months

A:

Q: Let 3z - 4x2 for z <0 3z2 + 3z forI20 | f(z) = { %3D ccording to the definition of the derivative, t...

A: Topic  =Limits

Q: Let f(x) = and calculate x(In(x)) f(x) dx by using integration by substitution. What was your substi...

A: Given that: f(x)=1x(lnx)6

Q: Find the minimum and maximum values of the function y = 2x-8x +7 on the interval [0, 5] by comparing...

A: Given that the function is        y = 2x2 - 8x + 7 on the interval [0,5] .

Q: Express the following functions in terms of function f where y=f(x). Professor Lapan's Helpful Hint...

A: We can solve both the part as below as per the instructions of Professor Lapan's Helpful Hint:.

Q: 1. Refer to the hexagon pattern below. ASsume that each edge of the hexagon measures 1 cm. Assume th...

A: H(n) be the function describing  the perimeter as a function of the shape number.

Q: 1. f(x) = -|x + 6| + 5 Range: x-int: у-int: Intervals on which f (x) is decreasing: Relative Extrema...

A: f(x) =-x+6 + 5                                      

Q: If x2+y?+z? = 9, dt dx dy = 7, find zp dt when (x, y, z) = (2,2,1). = 8, %3D %3D dt dz dt X when (x,...

A: Given x2+y2+z2=9dxdt=8, dydt=7     

Q: A corner of a portrait oriented A4 sized coupon bond in millimeter is folded over so as just to reac...

A: Given: A4 size paper with dimensions 210 x 297 mm  (general dimensions) The corner is folded over so...

Q: Transform the rectangular equation y = - 8 to a polar equation in T and 0.

A: