12. Sketch a picture of a graph y = f(x) that satisfies f'(-1) > 0, f'(0) = 0 and f'(1) < 0.

Q: х — 4 4. у х — 3

A: Given: - The function is, y=x-4x-3 To find: - Sketch a graph of the function. Label any intercepts, ...

Q: ; lim f(x) ; lim f(x) = 1. f(x) 51 曾()- X-1 2. f(1) = 4 3 3. lim f(x) ; lim f(x) ; lim f(x) %3D %3D ...

A: Topic =Limits

Q: 6. (3y2-x2" = 0 ;when x = 1, y = 1 y5 2y4

A: The given differential equation is 3y2-x2y5y'-x2y4=0; when x=1, y=1  

Q: dz 22. Evaluate the definite integral Hint: Trigonometric Substitution 2zv9z2-4 0.

A: To evaluate: I=∫03dz2z9z2-4...(1)

Q: Aradioactive chemical has a decay rate of approximately 5% per year Suppose that thès chemical is re...

A: The amount of radio active substance remains after t years is given by             A = pk1-e-kt     ...

Q: 3. ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A:

Q: Challenge Problem I a function / is inereasing on the intervals 3,31 and 11, 19 and decreasing on th...

A:

Q: dz du Evaluate the integral Jo 5 the concept J + c. 2zv9z2-4 using uvu?-a? arcsec a a

A:

Q: Evaluate | F • dr where F (0, y, – 4x), and C' is given by - F(t) = (t, sin(t), cos(t)), 0 <t<

A:

Q: 9. There is an infinite discontinuity at x = 0 and f(0) = -2 10. There is a jump discontinuity at x ...

A: 9. There is an infinite discontinuity at x=0 and f(0)=-210. There is a jump discontinuity at x=1 and...

Q: Find the MacLaurin series of f(x) = sinh(3x) . Express your answer in the form Σan (x - c)^n. The pr...

A:

Q: A dice is thrown What is the probability of getting 1- Get number 1 2- Get the number 4 3- Get an ev...

A: A dice is thrown. We have to find the probability of getting: the number 1 the number 4 an even num...

Q: 4x4 + 3 dx = 4x5 + 15x +2 1 + C 5(4x5+15x+2)² A) ++3x .5 + C 15 - x²+2x 2 (C In 4x + 15x+ 2+ C D) 5 ...

A:

Q: lim g(x) =, lim g(x) ; lim g(x) 1. -1- 34 2. g(-1) = 2- 3. lim g(x) = lim g(x) = ;lim g(x) = x0- 1. ...

A: Topic = Limits

Q: 7-4х 3. У 3 5+ 2х

A:

Q: A particle moves according to a law of motion s = f(t),t20, where t is measured in seconds and s in ...

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

Q: Find the total area of the shaded region. 1.5- (9.1) 0.5- 4.5 9. 13.5

A:

Q: O Find dy/dx, given y =. -u and u =TR42.

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to u

Q: Evaluate the integral using Trigonometric Integrals S (8 – - 3cos (x)sin°(x) dx °(x)sin´(x)dx

A: We can find the integration as below using trigonometric integral.

Q: Carite tan 24t.10x= 14 equlin fer a lie pepanicubr to Hhe pait (10.6) and

A:

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month i...

A:

Q: 3x2y + ey )dx + ( x³ + xev – 2y)dy=0

A: This equation is of the form Mdx+Ndy=0M=3x2y+ey ,N=x3+xey-2yChecking for exactness∂M∂y=3x2+ey ∂N∂x=3...

Q: 3 V9x2 + 4+2 In 4 1 dx 3x

A:

Q: Find dy/dx in terms of x and y if x²y – x – 4y – 9 = 0. dy dx

A: Here we will use the product rule for derivative d(uv)=u.d(v)+d(u).v

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Given

Q: Lauren plans to deposit $7000 into a bank account at the beginning of next month and $250/month into...

A:

Q: A(t) 8+ 6+ 4- 2- 10 15 20 25 30 The rate at which ants arrive at a picnic is modeled by the function...

A: Given query is to find number of ants in the given interval.

Q: For f(x) = 3x2+ 8x + 3, find the equation of the tangent line at the following values of a. (a) x = ...

A:

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconcl...

A:

Q: Find the indefinite integral. Include a multiplication sign between functions. For example, z e2. 21...

A:

Q: 1 (x+ 2) (3x² + 12x + 1) dx + 1) dz (А) (B) 4 (c) 7 (D) 252

A: Topic = Integration

Q: Evaluate the limits. Show your solutions. 1. lim lim 3. lim 北主 2.

A:

Q: Find f(a + h) – f(a) lim h→0 h If f(m) = m² – 4m + 6 O 2(2a-1) 4а-2 2а-4 2(a+2) None of the Choices

A:

Q: 17, सिद्ध कीजिये कि बिन्दु a-2b+5c,2a 46+7c तथा 3 (UP 2001) समरेखीय हैं, जहाँ a. b. c असमतलीय सदिश ह...

A: Let, the vectors be, u = a - 2b + 5c  v = 2a - 4b + 7c  w = 3c   

Q: 5. Consider the graph of y = f(x) below. On the same set of axes sketch a clearly labelled graph of ...

A:

Q: Differentiate (xy)* = e a. y' = Y(1+lnxy) c. y' = Y(1-Inxy) b. y' = x(1+lnxy) d. y' =Y(1+ln xy) y

A: (xy)x=e Take logarithm on both sides: ln(xy)x=lne ln(e)=1: ln(xy)x=1  

Q: 3. lim f(x) = -2, 4. lim f(x) = +∞, %3D I-2- x-3- lim f(x) = 2 and f(2) = 0 lim f(x) = -0 I-3+ %3D I...

A:

Q: 家, for x 2 2 3-x, 3. Given the function h(x) = Corrs graph and find a. lim, h(x) b. lim h(x) C lim h...

A:

Q: E valuate the improper integral Sma Xe* de Ina

A:

Q: Use transformations to graph the given function. 3) p(x) - -3x + 3| - 1

A:

Q: 1 9 – x2 (A In(v9 – a?) + C - B 응sin-1(품) + C (C 3sin-1(x 3 + C D) sin-그(프) + C 3

A:

Q: In the previous Problem Set question, we started looking at the position function s (t), the positio...

A: Solution ) s ( t )  = e 7t sin(2t) Velocity function v(t) = s'(t) [ we use product rule  {F(x) , g(x...

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to...

A:

Q: Let flx)-4x H2 %3D

A: Topic = Function

Q: Find the exact arc length of the curve x = y4/8 + 1/4y2 ,   1 ≤ y ≤ 3

A:

Q: (2x – 5, x 2 0 lim h(x) = x→-4 where h(x) = x + 7, x < 0 Table 1: x -5 -4.5 -4.1 -4.01 -4.001 approa...

A:

Q: Use the graph of f (x) = x below to find a number & such that x-1< 0.2 whenever 0 < |æ – 1| < d. %3D...

A:

Q: Vx2+4-2 lim x2

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 4. f(x) = x² + 4x 5 %3D -

A: As per our guidelines we are supposed to answer only first three parts.kindly repost others part as ...

Q: f'(t) = sin tf (t).

A: Given that: f'(t)=sin t f(t)...(1)