Suppose f and g are two continuous functions on [a,b] and that f(a) < g(a), but f(b) > g(b). Show that f(x) = g(x) for some x E [a, b.

Q: Write an inequlity comparing with +4 for n > 1. (Express numbers in exact form. Use symbolic notatio...

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Q: QUESTION 4 2 =16 3*+1 = 34 4.1 4.2

A: We, know that  ax=ay⇒axay=1⇒ax-y=a0⇒x-y=0⇒x=y

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A: Inductive reasoning: A general conclusion is drawn from a number of observations.   Deductive reason...

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A: Introduction: If a vector makes an angle with the positive x-axis, then, it can be decomposed into i...

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Q: 6. If a series Lu, converges to the sum u then so does any series obtained from Lun grouping the ter...

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Q: If P(ENF) = 0.0675, P(E|F) = 0.15, and P(F|E) = 0.3, then (a) P(E)= (b) P(F)= (c) P(EUF) =

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Q: Find the inverse Laplace transform L-{F(s)} of the function 2 F(s) = s2 + 9s – 10

A: Note:- L-11s+a =e-a t ; s&gt;-a   Given function is Fs =2s2 +9s-10

Q: (b) Find the area of the triangle whose vertices are A(0,0,0) ; B(1,1,1) and C(0,2,3). 1 (C) Find th...

A: Given (b) The vertices are A0,0,0, B1,1,1, C0,2,3 c(1) y=1x2-1 c(2) y=9-x2

Q: 2 + yexy y' 2у — хеху xexy ||

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Q: If the sum of first n even natural number is 420,find the value of n

A: Problem:- If the sum of first n even natural number is 420,find the value of n first n even natural ...

Q: Questions on Derivatives: 1. Use the limit definition of the derivative to exactly evaluate the deri...

A: According to our guidelines we can answer only one question and rest can be reposted. 

Q: dy (x + 1)+ y = In x dx У(1) 3D 10

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Q: ) Assume (X,A) is a Ealgebra and ld ycx be an anbitrary subset. Show that the Pami ly of sets 3{unyl...

A: σ-algebra: a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X, is closed under ...

Q: Find the Laplace transform of the given function. [1, 0 8 L{f(t)} s > 0.

A: To find- Find the Laplace transform of the given function. ft = 1,0 ≤ t &lt; 80,t ≥ 8     Formula Us...

Q: Use generating functions to determine the number of 9-digit sequences of the digits 1,2,3,4,5,and 6 ...

A: We need to find ,  number of 9-digit sequences of the digits 1,2,3,4,5,and 6 in which each even digi...

Q: Is the series 22"31-" convergent or dive n=1 Co

A: Introduction: We know that the series an=∑an converges only when L&lt;1, diverges when L&gt;1, Where...

Q: Problem 3. First verify that y(x) satisfies the given differential equation. Then determine a value ...

A: The solution of the equation is defined as the function that satisfies the differential equation. In...

Q: la) show that the necessary & sufficient condition VE constant to be constant gcodesic on EE, +FE, -...

A: Geodesic Curve: Let A and B be two given points on a surfaces. Let these points be joined by curves ...

Q: Find the expected value for the random variable: 4 6 Р(X) 0.21 0.28 0.14 0.37 E(X) = %3D

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Q: Solve the initial value problem. y" – 2y' + 2y = e; y(0) = 0, y' (0) = 4

A: Given differential equation is y'' -2y'+2y =e-t;  y0=0, y'0=4 Take "t" as independent variable.

Q: Directions: Justify each statement by stating the property, theorem, postulate, or definition that s...

A: 4) The statement is "If x&lt;10, then 4x&lt;40". The property depicted here is the multiplication pr...

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since th...

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A: Given,             R=(1; 2); (1; 6); (2; 4); (3; 4); (3; 8)S=(2; u); (4; s); (4; t); (6; t); (8; u)

Q: dout 2 *Property of STI Page 2 of 4 IT1903 Rounded - Since the problem states each Round – off Error...

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Q: Using integration by parts, find the Laplace transform of the given function; n is a positive intege...

A: Given f(t)=tneatwhere n is a positive integer and a is real constant. We have to find the Laplace tr...

Q: Use ß- function deźinifion af pirivative to Prove that f is differentiable at2, then f is continnos ...

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Q: a dilation by a scale factor of 3 centered at the origi

A: In this question, the concept of dilation centered at the origin is applied. If the center of dilati...

Q: Problem 3. First verify that y(x) satisfies the given differential equation. Then determine a value ...

A: The given question is related with differential equations. Given that,                   y' = x - y ...

Q: 4000 3500 3000 2500 2000 1500 1000 500 200 250 300 350 400 450 Number of Customers Number of Custome...

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Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in...

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Q: An airplane is heading north at an airspeed of 600 km/hr, but there is a wind blowing from the south...

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Q: C. Find the volume of the solid whos base is bounded by the graphs y%=1and y=x-1 The crosS sections ...

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Q: Use the inverse method to solve 2.x1 + 3.x2 = 3 5.x1 + 4.x2 = 11

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Q: Lindg @ X= L

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want...

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

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Q: Fine the mean number 12 31 45 67 78

A: Mean number is defined as the value calculated by dividing the sum of all the values by total number...

Q: [et Suppose A(t) =0 0. cos t sin t, show that A(t)-1 exists and then find it. - sin t Co t. -

A: Given- At = et000cos tsin t0-sin tcos t To Show- Show that At-1 exists and then find it.

Q: Determine whether the improper integrals converge or diverge. If possible, determine the value of th...

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Q: Find the Equation of the line that passing in point (3,5) and parallel or perpendicular to the 4x-y=...

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Q: =1 using Cauchy's Residue theorem.

A: Cauchy's Residue theorem: Let fz be analytic within and on a positively oriented simple closed conto...

Q: 4-Vx lim х-16 16х-х2

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Q: 16. Prove: If A is an eigenvalue of A and x is a corresponding eigenvector, then s) is an eigenvalue...

A: We will use definition of eigen vector to prove the result.

Q: 3*4=5 9*1=2 6*4=2 9*3=0 Then5*8= ____?

A: Introduction: Pattern identification is a tricky part of mathematics. From the given numbers, first,...

Q: (t2 –1 if t < 5 (2kt The value of k to make the function f(t) continuous at t-5 is if t 5

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Q: prove that C+Ã +3 = ARC Using the truth table

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Q: 2. What is the number of k-digit strings one can form over an n-element alphabet if (a) there are no...

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Q: - Compute the volume of a hemisphere by numerical integration using the lowest order Newton-Cotes me...

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Q: The autonomous DE: dy +5=y-4 dx has an unstable critical point at y =4. Select one: True O False

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Q: 2. Using the iteration method to find the approximated root of the following equation: (x-1)e-1-0 Co...

A: Given: The equation, x-1ex-1=0 and the iteration equation, xk+1=1+e-xk.   To show: (1.) In the inter...