Find fg where f (x) = x² + 1 and g(x) =x + 2 are functions from R to R. a) x² + 1x + 2. b) x + 2. c) x? + x + 3. d) x³ + 2x² + x+2. e) None of the above. O A) O B) C) D) O E)

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: Prove the following Quotient Rule, where f, g are differentiable:

A:

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A:

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: 3. Find and sketch the domain of f(x, y) = In(9 – x² – 9y²). [Hint: In(x), x > 0]

A:

Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: . Use the definition of error function, prove that [²' ( ²² ) = √T z

A: On solving this we will get

Q: Let f : R" → R with f(x) = /1+ ||x||?. Show thatf€ C.

A: As per the question we are given a multivariate function f from Rn to R , and we have to show that :…

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: f(x) = x2 + 5x − 4 is a polynomial so it is continuous for all values of x so it will be continuous…

Q: Use the Squeeze Theorem to show that f(x) = x² is in R[0, 3]. %3D

A:

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: The Intermediate Value Theorem that states if a function f(x) is continuous and k is     any…

Q: • The Doman of f(x) = 4-Vx is 1. (2, co) 2. [-2, c0) 3. [2, 0) 4. [-2,2]

A: The domain is the set of all values of x for which the value of function f(x) exists.   For f(x)=4-x…

Q: In Exercises 3–8, compute f'(a) in two ways, using Eq. (1) and Eq. (2). 3. f(x) %3D х2 + 9х, а%3D0

A:

Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

A:

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

A:

Q: 2. Let f : (0, –→R such that f(x) = x². Show that f(x) < r. • Show that f has no fixed point on (0,…

A: The given function is f:(0,13]→R and defined as f(x)=x2 . we have to show that f has no fixed point…

Q: Let f(x) = x² Inx. Use the Three-Point central Formula with h= 0.2 to approximate f"(1.5) %3D %3D…

A: Given that, f(x)=x2lnx and h=0.2. The three point formula for second derivative is given by,…

Q: 10.30

A:

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: Given: The function, fx=x2+5x+1, 0,8, fc=25.

Q: - R-{-}→R-{} defined by f(x) = Show that f: R 3x-5 2x+1 is bijective.

A: Given function is f: ℝ - -12 → ℝ--32 such that f(x) = 3x-52x+1

Q: (a) Verify Rolle's Theorem for f(x)= 3x – 12.x + 4 over the interval 0, 2

A: Verify rolle's theorem

Q: Find and sketch the domain of f(r, y) In(r - y) 6. -

A: Given:      f(x,y)=lnx-y9-x2-y2·x2+y2-4    Interval notation : -3,0∪0,3   Set builder notation:…

Q: Show that the function f(x)=3x-2 is a bijection.

A: For a function is to be bijective, then the function should be well defined, surjective, and…

Q: Exercises 19–22, show there is a number c, with 0 ≤ c ≤ 1, such that f(c) = 0.  19. F(x) = x3 +x2- 1

A:

Q: Show that (f) and () aoe invesse fondion ARgeboaically @ fix) fex) = " O f cx) = X- I X+5 g(x) = ニ

A: We have to show that f and g are inverse function.

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: Verify that the function satisfies the three hypotheses of Rolle as a comma-separated fist.) x) = 3x…

A:

Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: (a) Prove the following relation: В (x + 1,у): B(x, y) x +y %3D

A: We have give Beta function relation, we have to show left hand side is equal to right hand side.

Q: 7. Find the minimum of, f(x1, x2) = 2x? – X1X2 + 2x³ + x³ – 2x1x3 And check the second order…

A: This is a problem of multi-variable calculus.

Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A:

Q: The value of c of f(x) = 2-, in the interval (1,3) such that f'(c) = %3D f(3)-f(1) %3D is 3-1 V340…

A: Given fx=2-3x given interval 1,3 f'c=f3-f13-1

Q: Glven that f() = 6x + 2 and g(x) = 1 - x, calculate

A: Given, f(x)=6x+2g(x)=1-x2f[g(x)]=f(1-x2)          =6(1-x2)+2          =6-6x2+2          =8-6x2Hence,…

Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: Intemediate value theorem gives that if f(x) is a continuous finction within the interval a, b  then…

Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

A:

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: 3. Prove F (Vr)(A→ B) → (Vx)A → (Vx)B. ->

A:

Q: Determine whether the functions is a bijection from R to R. f (x) = (x + 1)/(x + 2) +

A:

Q: Use Green's Theorem to evaluate F dr, where F(2, y) = (9xy, y" - 8) and C is the rectangle with…

A: That's easy. Have a great day!!!

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: It is given that, f(x)=x2+6x+1  , 0,5 and f(c)=28By verifying the intermediate value theorem applies…

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: Given f(x) = x2+6x+1 , 0, 8, f(c) =28Here we verify that the intermediate value theorem applies to…

Q: Use FTC I to prove that if |f '(x)| ≤ K for x ∈ [a, b], then |f (x) − f (a)| ≤ K|x − a| for x ∈ [a,…

A:

Q: Apply the Intermediate Value Theorem in the indicated interval and find the value of c guaranteed by…

A:

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.