Question 14 Let z(t) be the solution to the following initial value problem (IVP) = (7z - 3)(2z – 1)²(3r -- 2)(z – 1). z(0) = 0.99. What is the value of lim z(t) %3D dt 01 Mack

Q: 1. sin(2x) lim X = 0 4х x° – 2x + 1 f(x) - x* + 3 Find all zeroes of f 2.

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Q: b. limx>-2 f(x) = -00 c.f' (0) = f' (3) = 0

A: b let fx=1x+2limx→-2fx=limx→-21x+2limx→-2fx=-∞so function is fx=1x+2

Q: Consider the following problem : dy dre 2 = (y² - 19y +90) sin² (2πy), y(0) = a а 19 Innitial value…

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Q: (a) Define the following hyperbolic functions directly in terms of the exponential function (ii)…

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Q: In a following chapter we will be able to show, under certain assumptions, that the velocity v(t) of…

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Q: Given that lim s→c f(s)=7 and lim s→c g(s)=−15, find each of the following analytically Give exact…

A: Given: lim s→c f(s)=7 and lim s→c g(s)=−15 Now,…

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

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Q: Suppose we know that y x ER, h(x) ç f(x)Eglx) where Determine lim flxl. X -)0 h(x)= 31-4x2 and 9(x)…

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Q: t² + 1 t 1 %3D lim→1- h(t) = ?

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Q: 8. lim xx = 1 00-X 9.lim (1 – 2x)x = e¯2

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Q: (a) Find the following: x1/3 + 9x/5 i. Lim X0 6x/2 - 4x1/4 (2x – 1)'/² – 3 ii. Lim X-5

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Q: (c) 1 lim – cos(6r) 5x

A: Explanation of the solution is given below...

Q: f(x) = x+1 g(x) = log(102tan¹(x)), h(x) = x . 1) Find lim f([h(x)]²) X-1 2) For the following…

A: Step 1:Step 2: Step 3: Step 4:

Q: 6. Find lim1F(t), where r(t) = 1² In (2t - 1) 1' 2022-t (1=1) 1/1₁ eve).

A: Answer and explanation is given below...

Q: (h – 2) - 4 (i) lim 2h

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Q: According to the Michaelis-Menten equation, when an enzyme is combined with a substrate of…

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Q: 10. True or false: the function y= 9=0 horizontal asymptote Jinz (x) x²+3 a has

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Q: x3+8 Q1: Find lim X-2 x+2 Q2: Find for y= (*)G + 4) Q3: Find for y= sin2x cosx +x lin(x) dy dx

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Q: x2+1 is: 15. The slant asymptote of f(x) = is: x+3 %3D A) y = x. B) y = x – 3. C) y = x + 3. D) y =…

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Q: 3; 1. lim Nx²+I - x4 +1

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: Cost (e) lim r t2

A: L'Hospital rule is a method to evaluate the limit of a rational function at a given point. The…

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

Q: 6. (a) Solve the equation dy dx You may leave your answer in an implicit form (i.e. you do not need…

A: (.)  Given differential equation is,             (.) Method of seperation of variables:A equation of…

Q: an =  (8n − 2)! (8n + 1)!   a1 =   a2 =   a3 =   a4 =   a5 =     lim n→∞ an =

A: Consider the given nth term an=8n-2!8n-1! Since, 8n-1!=8n-1 8n-2! So, an=8n-2!8n-1!=8n-2!8n-1…

Q: 1 lim 1 = 1 2"

A: The given limit is limn→∞1-12n=1.

Q: 4 lim t 4/11+ a. %3D 44 t2 - 16t - b. lim %3D t 4/11- 44 t2 - 16t DNE lim t 4/11 С. %3D 44 t2 - 16t

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Q: If 0 < a < b, find 37 (br + a(1 – x)]' dz lim

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Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

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Q: х — 1 lim х-1+ V2x-x2 1/

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Q: Could you use L'Hopital's rule to solve the following question in its current form: lim,0+ In(x+1) O…

A: We have one of the following form limx→af(x)g(x)=00 or  limx→af(x)g(x)=±∞±∞  In these cases we have…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.