Find dy dx ; 1) y = 1/3 tan x/m

Q: 1-cos (3x) x² a) lim- X-0 xm-am x-a x-at b) lim 1-c0SX X=0 X+COSX c). lim

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Q: 17 a) Let ~= and √²=, Sketch in standard. Suitable triangle Position in 30, and use to find the…

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Q: How do you integrate In = ∫yne5ydy ?

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Q: dt = 8x - x² Identify the equilibrium points Determine if the equilibrium points are stable or…

A: Since you have posted a question with multiple sub parts, we will solve the first four sub parts for…

Q: (13%) Problem 7: A shopper standing 2.5 m from a convex security mirror sees his image with a…

A: The objective of this question is to find the image distance, focal length, and radius of curvature…

Q: 2. A nilpotent matrix is a square matrix A € Mnxn (F) such that Ak = 0, for some integer k. -3 1 0 2…

A: Solution for (a): Show that the matrix �B is nilpotent.Step 1: Understanding Nilpotent MatricesA…

Q: 1) Suppose you take out a $100,000 loan from a bank, with an interest rate of 13.5% per year…

A: To solve this problem, we can use the formula for the present value of an annuity:Where:PV is the…

Q: 14. Give a careful proof that the graph below is not planar. Hint. The girth of the graph is 4.

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: {}} 2. L-1

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Q: A = [[a,b][c,d]] Assume ad-bc≠0   Show that A is row equivalent to the identity matrix (Hint: divide…

A: The objective of the question is to show that the given matrix A is row equivalent to the identity…

Q: Define a function f: N → Z by n/2 (1-n)/2 f(n) = { (a) Show that f is one-to-one correspondence. (b)…

A: We need to show that if , then .Let's consider two cases:Case 1:  and  are both even…

Q: 10. The loudness, L, of a sound in decibels (dB) can be calculated using the formula L = 10 log(+),…

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Q: Solve: y''-xy'+4y = 0 With the power series method

A: Given:Given differential equation is

Q: The Gompertz model is a classical model of tumour growth where a is a growth rate and b is the…

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Q: (3) Which of the following matrices are invertible? Justify your answers. You will get no marks for…

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Q: Oppgave 8 Finn summen av rekken uttrykt som en funksjon. 1 1 1 2².2 23.3 24.4 1 2 n=1 1 21 n

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Q: For a recurrence equation given as: an = 7an-1 - 10an-2 for n > 1; a0 = 2; a1 = 1 Identify the exact…

A: Given recurrence relation  for

Q: 1 -6 7 Let A = 0 2 X 3 and b L2 -12 14] If possible, write b as a linear combination of the columns…

A: We have to check  as a linear combination of the columns of A or Not.

Q: 2. The following pair of points (Table 1) result from an experiment. Table 1: Data points for…

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Q: 1. Which expression is equivalent - s [172 COS

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Q: 7. Solve the following. Check for extraneous roots. a) log(x + 25) = log₂(x − 1) = 3 b) log x + log…

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Q: x+2 L. Solve 3*+² – 3* = 24 √√3. Leave answers in exact form, then round to 2 decimals.

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Q: Problem 2. Let A & Fnxn be a fixed matrix. Define the following set IAC F[x] as follows: IA =…

A: Answer:1. Yes, IA is an ideal due to the closure properties mentioned above.2. The minimal…

Q: Recent technological breakthroughs now allow greenhouses in Ontario to grow tomatoes during winter…

A: The objective of the question is to find out how long the gardener should keep the water flowing in…

Q: 8 s=2 s(s + 1) s2 + 1 75-1 = 00 Σ m=# C(m) xm

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Q: 4^2+15^2-3^2

A: We have to find the value of 42 -32

Q: If f(x) = f'(2) = g(x) h(x)' then

A: Given .We have to find

Q: Find the general solution of the differential equation: dy - 2ty + 4e-t². dt What is the integrating…

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Q: Let {9} SCR³, is S a spanning set for R³? That is, does span(S) = R³? S = Is S from the previous…

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Q: We are trying to prove that a proposition P(n) is true for all n≥0 using mathematical induction. We…

A: The objective of the question is to understand if the same result of a mathematical induction proof…

Q: 5. 3 0 1 -3 0 2 1 4 0 -1 4 0 0013 3-4 * * 2-6

A: We will reduce the given matrix.

Q: 6.5.1 Learning Goal: To be able to calculate the moment of inertia of composite areas. An object's…

A: The composite area consists of a rectangle, a semicircle, and a triangular cutout as shown in the…

Q: Consider the following graph. List all the paths between vertex A and vertex J and do not visit any…

A: For the given graph,1). List all the paths between vertex A and vertex J.2). There are two circuits…

Q: Revenue, Cost, and Profit Yaster Electronics manufactures and sells a televisions per month. The…

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Q: Find the state vector X3 for the given stochastic matrix A and initial state vector Xo. A = 31 0--0…

A: Let x0 be the initial state vector. We need to find the state vector x3.Given the stochastic matrix…

Q: 1. Let u = [1 0 1]",0₁ = [1 1+ T -i]¹, 1+i 1- - V₂ = [2i 1 0], and v3 V3 = [2 −1 1]². Let = V1, V2,…

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Q: What are the units of S'(13)? millions of dollars per year months millions of dollars dollars per…

A: We have to find the units of S'(13).

Q: J Assume E₂ and E₂ one measurable. Without using the fort that the Union of measurable sets in…

A: Given that  and  are measurable.We need to prove that  is measurable.We know that .We know that, if…

Q: (a) Show that y₁ = r² is a solution of x²y" 3xy' + 4y = 0, Then use the method of reduction of…

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Q: What is the average volunteering time for females and males?[OBJ ........What is the value of t?....…

A: The objective of the question is to calculate the average volunteering time for males and females,…

Q: You are considering to produce two kind of candies: Candy1 and Candy2, both of which consist solely…

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Q: If no payments are made, a loan of amount $36000 would increase to $43070.89 after 2 years of…

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Q: Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard…

A: (a)We have given VariableObjective coefficientsAllowable IncreaseAllowable…

Q: (c) (For this question, assume that a function f and a number b are given). For every > 0 there…

A: i)  the symbol logic for this statement is  ii) Now the negation of the statement without negation…

Q: 2. Consider the function f : [0, 1] → R, 1 { f(x):= if 1 < x≤ for some n E N n+1 if x = 0 Prove that…

A: To prove that the function f:[0,1]→R is Riemann integrable on [0,1], it can use the Riemann…

Q: Sketch the curve traced out by the vectorvalued function. Indicate the direction in which the curve…

A: Let F:R2→R, and the parametric equation given is , for t≥0.Since, there are 3 components to F(t),…

Q: Given a velocity field: V = 1.8 ( rz (1-sin²(0))) er + 2.8 (1-cos2(0)+ rz) eg +1.8 ( rz tan(0)…

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Q: For the following types of quadrilaterals, give the possible number of nonzero distance it can have.…

A: The objective of this question is to determine the possible number of nonzero distances in two…

Q: 0 0 0 32 4. 0 1 3 3-2 1 2 2-4

A: We will reduce the given matrix.

Q: +{}} 4 S 2. L-1

A: Here we use F(s) = f(t) = Here we know =