dy The following problem involves an equation of the form dt = f(y). Sketch the graph of f(y) versus y, determine the critical (equilibrium) points, and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. dy = y(y – 3)(y – 6), Yo 20 dt |

Q: uate lim t→+∞\ 3t2 + 2

A:

Q: The number of bacteria "N" present in a culture increases at a rate proportional to the number prese...

A: Topic:- function

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

A:

Q: There is a jump discontinuity at x = 1 and lim f(x) = 1

A: At X=1, there is a jump discontinuity.   limx→1- f(x) = 1.As function f(x) approaches towards 1 from...

Q: Answer 2 only

A: In this question we will use basic concepts of calculus i.e concepts of integration. Solution of the...

Q: 1.84 We call pa cluster point of E, provided that for all e > 0 there exists e e E such that 0 0 th...

A: We have to show E has no finite sub cover. 

Q: V3 2 dy 1- у?

A:

Q: -5 -4 -3 -2 -1 -2 -4 Find the following. lim f(x) = lim f(x) lim f(x) = f(1) =

A:

Q: 2x 26. Evaluate / sec (= tan 5 dx and determine its particular antiderivative whose y-intercept is 2...

A:

Q: 1.3 + j4 2. –3 + j4 3. –3 – j4 4. 3 - j4

A:

Q: Obtain f (x) as a polynomial in x using Newton's divided difference formula for the following data. ...

A:

Q: The temperature, in degrees Celsius, at a point (x,y) on a metal plate is given by T(x,y) = 20-4x^2 ...

A: Given Temperature on a metal plate at point (x,y)T(x,y)=20-4x2-y2

Q: ax2ª(x2a+1)°dx

A:

Q: Determine the convergence or divergence of the series. 1 a) E п+3 n=1 1 b) E 2" n=1

A: topic -  series convergence and divergence test  

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0, ...

A:

Q: ydx+(2x+3y)dy=0 solve by using homogeneous equaations

A: We know,∫dxx=ln(x)   Given differential equation, ydx+(2x+3y)dy=0 ⇒dydx=-y2x+3y....(i)  

Q: Find the derivative of 7 (t) = (1+t°, te¯t, sin (2t)) A. F'(t) = (3t°, (1 + t)e¯t, 2 cos (2t)) B. 7(...

A: We are asked to find the derivatives.

Q: 3. lim (3 Vx + 9/

A: This is a problem related to limit of the function. Based on the general formula of limit or using L...

Q: 1 2x-9 13 Evaluate lim 1 x→-2 - 2x+8 4

A:

Q: INTEGRAL Evaluate the following: e 20do 10. ↑ 1+ 3e20

A:

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A:

Q: dt dx 3. 6x – x² 4. sin xV1 XN Cos xdx 3x 5. 1-2e3*) 6. dx

A: We solve only 4th question.  Let 1-cos(x) =t 

Q: Use the Laws of logarithms to rewrite the expression x°y13 log zl1 ,5,13 in a form with no logarithm...

A: Given query is to find the value of A,B and C.

Q: Confirm that the integral test is applicable and use it to determine whether the series converges. 1...

A:

Q: Instruction: Solve the following indefinite integrals. Show complete solutions. 14. | csc(1 + sin? x...

A:

Q: e) 1 Σ Vn n=1 3 f) 5 3 п-1 п 8 W

A:

Q: x'e-2x dx 20 dx 2

A:

Q: Which of the following is the general solution to the differential equation y?dx = (xy – x²)dy? x In...

A:

Q: 23. What is dx? 3 – e4r e2z + V3 In e2r + V3 In |e2x а. +C C. +C 2 e2x – V3 V3 /3. b. V3 +C V3 +C 2x...

A:

Q: Using the graph find the following: (6.5) a. lim f(x) e. lim f(x) X-4 (4.2) f. lim f(x) (2). (6.2) b...

A:

Q: Let z = 6exv , find dz %3D

A:

Q: dy = ay + b whose dt Write down a differential equation of the form 3 as t → o. 4 solutions all appr...

A:

Q: • f(x) = -1 when r 2 • f(0) = 1. 1 2 ) Define the function f on the interval [-2,2] such that f is ...

A: (i) We can take fx=x+1-2≤x≤0-12x+10≤x≤2. Note it is obtained by connecting the known points via line...

Q: Determine the constants A, B: 2.х — 3 A В (x – 3)(x – 4) x – 3 x – 4 - - +

A:

Q: Use substitution to evaluate the integral | (3x³ + 5)° . 27x²dx

A:

Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: Find the area of the region bounded by the parabola y=5x^2, the tangent line to the parabola is at (...

A:

Q: For the given p-series, identify p and determine whether the series converges. Ek-615 -6/5 k=1 . The...

A: Find your answer below 

Q: The exponential growth model of a population in a certain city is A= 20e0.05t where A is the size of...

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost o...

Q: 2/3 if fox)= 3x- point A(8,2) to B (27,17) l0, find the length of the graph of f frome

A:

Q: Find the inflection points of each of the given curve.  y = 5x – x5

A: Given :y=5x-x5

Q: Consider the following. cos(x) + Vy = 3 (a) Find y' by implicit differentiation. y' = (b) Solve the ...

A: Derivative

Q: Find the indefinite integral. 4x2+2x-1 d.x none of these Omz + 1| -31m|z미-글+C o+ Inz* + =*|+C In a+1...

A: Given: I=∫4x2+2x-1x3+x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫1ax+bdx...

Q: da (cos ( 3x) sin( 2æ)) dæ

A:

Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4 pound...

A:

Q: Eliminate c, x'y =1+ cx (2+x3y)dx + xdy = 0 B (1+x?y)dx + x³dy = 0 © (1+x?y)dx + x²dy = 0 D (1+x3y)d...

A:

Q: аx2а (х2а+1)* dх ax²a

A:

Q: Find the equation of the tangent line of y = 4e* at xo = 0. (Use symbolic notation and fractions whe...

A: y=4exSubstitute x=0y=4e0=4The point is (0,4)

Q: Let F(x,y,z) = (y,x²,zy) where C:R(t) = (cost,sin t , 3t) and t e [0,2]. Evaluate %3D %3D •dR

A: We have to find value of given Integral.

Q: possible rational zeros given by the rational zeros theorem (but don't check to see which actually a...

A: