3, 5x 60(x 2 + x;), 3 b) Y = In 7.

Q: Use Linear Approximation to estimate Af = f (7.01) - f(7) for f(x) = x². (Use decimal notation. Give…

A:

Q: 1. Verify that the Mean Value Theorem applies to the function f(x) = v25 – x² on the interval [-3,…

A: Use mean value theorem

Q: Using the Constant Multiple Rule InExercises 25–30, complete the table to find thederivative of the…

A: The given function is, y=5x2-34. The objective is to find the derivative of the function by using…

Q: 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not…

A:

Q: Use Linear Approximation to estimate Af = f (3.01) – f(3) for f(x) = x*. (Use decimal notation. Give…

A:

Q: alue Theorem to approximate the value of

A:

Q: Show that f:Z-->Z ; f(x)=x+2 is invertible

A:

Q: evaluate using the appropriate method or combination of methods.

A:

Q: 3. Verify that the function f(x) defined over the interval [0, 3], satisfies Rolle's theorem. Find…

A:

Q: 2) Verify that the function f(x)=x'-x satisfies the hypotheses of the Mean Value Theorem on the…

A: We have to check the conditions for Mean Value Theorem.

Q: The function f, where f(x) = secx, has domain 0<x< and has inver %3D f-l, where f-(x) = sec-lx. Show…

A: The given function is f(x)=sec x and the inverse function is f-1(x)=sec-1x. To prove that…

Q: Verify the applicability of the intermediate Value Theorem in the indicated interval and find the…

A:

Q: 2. Find a function f and a number a such that f(t) -dt = tanx. Give proper reasoning.

A:

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

A: Integral is F(x)=∫4xt32dt

Q: Use the Linear Approximation to estimate Af = f(4.8) – f(5) for f(x) = x – 5x². (Use decimal…

A: Given data:   The given expression for the function is f(x)=x-5x2. The given value a=5.   The…

Q: 6 Evaluate JVx7 – 7x5 + 17 Vx1ºdx -

A: To solve the given integral.

Q: ) Show that the function f(x) = x 2 − 4x + 3 = (x − 1)(x − 3) satisfies the conditions of the Mean…

A: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

Q: Use the mean value theorem to prove that v1+ x 0 *Hint*: Apply to mean value theorem to f(x) = /1+x…

A: let f(x)=1+x2-1+xnow differentiate f(x) w.r.to x, we get f'(x)=12-121+xtherefore ,…

Q: 4. Check that the function f(x) = x3 satisfy the hypothesis of mean value theorem or not at the…

A: To check that f(x)=x4/5 satisfies mean value theorem or not on [0,1]

Q: Find the area in square units of the region under the graph of the function f on the interval[-10,5]…

A: By fundamental theorem of calculus area of square is A=∫-1055dx=5x-105⇒A=55+10⇒A=75 square unit

Q: Use Linear Approximation to estimate Af f (2.05)-f(2) for f(x) = %3D x+I (Use decimal notation. Give…

A:

Q: Use the Linear Approximation to estimate Af for f(x) 5+x2 when a = 2 and Ax = -. (Use decimal…

A: Given :   f(x) = 11  / 5+x2     a = 2     ∆x = - 1/2 = -0.5

Q: Explain why the two forms of Green’s Theorem are analogs of theFundamental Theorem of Calculus.

A:

Q: 6. Verify Mean Value Theorem for the function f(x) = 3x² -4x +5 in [-1,1].

A:

Q: Explain Fubini’s Theorem.

A: Fubini's Theorem: If f(x, y) is a continuous function on a rectangle R=[a, b]x[c, d] then the double…

Q: of

A:

Q: To prove L'Hopital's Rule for the case, you use what Theorem and what statement is a direct result…

A: For ∞∞ case, we can use the l'Hospital rule by taking the derivatives of numerator and denominator…

Q: Use the linear approximation to estimate Af = f(3.2) – f(3) for f(x) = 1+x² * (Use decimal notation.…

A: Given: f(x)=81+x2

Q: Continuous everywhere

A: The following are theorems, which you should have seen proved, and should perhaps prove yourself:…

Q: Regioin bounded by x-g and X=24-9

A: Area bounded by the curves, Using the double Integrals

Q: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

A: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

Q: Apply the Mean Value Theorem (i.e., find the possible c-value in [-12,0]) on the function f(x) = V4…

A:

Q: Use relevant definition(s) and theorem(s) to prove the fundamental theorem of calculus part 1.

A:

Q: Verify that the function f(x)= x-3x+2 satisfies the hypotheses of the Mean Value Theorem 6. on the…

A: Known fact:

Q: It is fact that the Mean Value Theorem (MVT) can be applied to the function f(x) = x2 + 2x -9 on the…

A:

Q: Assuming Stirling's formula, show that 1%=Vx + 1)-f(x – 1)] - (x+ 2) – ƒ(x– 2)] upto third…

A:

Q: Realize Mean Value theorem of the function f(x) = x + 1/x on [1/2,

A: We will solve the problem

Q: 4. Verify Mean Value Theorem for the function f(x) = 2x ° - 6x2 + 2 in the interval %3D [a, b],…

A: given function :

Q: Verify Lagrange's mean value theorem in f(x) = x²+2x-1 in (0,1)

A: We have ,  f(x) = x2 + 2x - 1    We know the , Lagrange's mean value theorem, If a function f is…

Q: Verify that the function satisfies the two hypotheses of Mean Value Theorem on the given…

A:

Q: 4. Verify Mean Value Theorem for the function 3x2 – 4x + 5 in [-1,1]

A:

Q: Verify the Mean Value Theorem for f(x) = In(6x + 1) on | 0, %3D

A:

Q: Find fqix(q|x) for x € {0,1} and all q.

A: Given Information: Q be the continuous random variable with pdf, fQ (q) =6q(1-q)       ; 0≤q≤10…

Q: - the use write down Calculus in econamicd.

A: Use of Calculus in economics

Q: Verify that g(x) = x/x+1 satifies the Mean Value Theorem on the interval [0, 4]. Then find the value…

A: Given:

Q: Show that cosh x> 1 + x² for all x.

A: comparison

Q: ENRI Green's theorem to

A:

Q: Use Linear Approximation to estimate Af = f (2.01) – f(2) for f(x) = x“. (Use decimal notation. Give…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!