10. Let f be the function from R to R defined by f(x) = 3x + 2. Find f-{-3,1,7}) a){- 55 3'3' 3 b) '5'23 5 5 5 3' 15 1 c)

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: What is the domain of the following function? f(z,9) 4-2 - y - In(y - z) + sin(z) +y 24 and y> =)…

A: Domain.

Q: Suppose that f: [0,1]–R is a function satisfying the conclusions of the intermediate value theorem.…

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Q: 1. Use the Cauchy-Riemann conditions to find out whether the following functions are analytic. a.…

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Q: Compute P(0), and find the exact values of the six circular functions given that 0 = – 135°.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Show that F = ху, , zy) is not conservative. 2

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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: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

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Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: Please

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Q: Estimate the value of f, (1 – r 4.r + 2x) dr using single application Simpson's 1/3 Rule.

A: This is a Numerical Analysis problem.

Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: (b) Show that the u(x, t) can be written as u(x, t) = 0(x – at) + 4(x + at), where o and are…

A: The multivariable function u(x,t) is a rule that associates or fixes a number to a particular point…

Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: Find the length of f(r) = on the interval [1, 2]. Show all calculations. %3D

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Q: Suppose f(x) = – 2x – cos r. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: 3.Show, by means of the example f(t) = sin t, that f ∗ f is not necessarily nonnegative.

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Q: (5) Find the most general function f(t) so that the curve F(t) =, shall lie in a plane.

A: The most general function for f(t) is a constant function, f(t) = c:   &lt;a cost, a sint, c&gt;

Q: Let f and g represent differentiable functions such that f ″ ≠ 0 and g″ ≠ 0.

A: Concavity of a function can be determined using the second derivative of the function. If the second…

Q: A function, F: R × R ---› R x R has been defined as follows: F(x, y) = (3y - 1, 1 - x) for all (x,…

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Q: Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

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Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Suppose f  is twice differentiable on R  and has threeroots. Show that  f " has at least one real…

A: According to Rolle's theorem, there is a zero of f'x in between two zeroes of f(x).

Q: Let f be the function defined byf (z) = 3z2 -z. What is the absolute minimum value of f on the…

A: Topic = Application of Derivative  The absolute minimum value of f is 0.

Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

A:

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: let s(t)=3sin(2t)+5. find the absolute maximum and minimum of the function on the interval [0,2pi]

A: We have to find

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: 3. Consider the function Prove that f'(0) = 0. & f(x) = if r EQ if x & Q.

A: Introduction: A differentiable characteristic of 1 actual variable is one whose spinoff takes place…

Q: 5. Verify first that the Intermediate Value Theorem applies to the indicated interval and find the…

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Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

A: To Determine: fins a and b so that the function is continuous and differentiable given: we have a…

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: GRuen that the divectional deivative of f(x,4,2) out the point (3,-2,1) in the divection of a=…

A: Given a→=2i^−j^−2k^ and directional derivative of fx,y,z at the point 3,-2,1 in the direction…

Q: Compute P(0), and find the exact values of the six circular functions given that 0 - 135°. = -

A: θ=-135° Now x-coordinate of Pθ is, cos-135°=cos135°   ∵cos-x=cosx=cos180°-45°=-cos45°…

Q: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…

Q: Verify that Rolle's Theorem can be applied to the function f (z) = 23 – 10z2 +27x – 18 on the…

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Q: prove that if f(x)is derivable at a point say "a" then it is continous at x=a

A: Here we have given that the function fx is diffrentiable at a point  .x=a that is f'x exists.…

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

A:

Q: Let f = f(x, y), x = s +t and y = s - t. Show that (9- ) - se se as at ax ду

A: It is given that, f=f(x,y), x=s+t and y=s-t. Show that, ∂f∂x2−∂f∂y2=∂f∂s·∂f∂t.…

Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: 4|x| – 3 pour x 1, x² – 4 f2(x) + V2 + x², || ||

A: Given that, f1x=4x-3x≤1-3xx2-4x&gt;1f2x=1+2+x2 To determine set of points which they are derivable…

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

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Q: Determine if f(x)=x² is uniformly continous on the interval I = (-∞, +)

A: See the attachment.

Q: Let f be in R[a, b]. Prove that -- f is in R[a, b] and ∫a b -- f(x)dx = -- ∫ab f(x)dx.

A:

Q: 2. Let f(r)= r on (0,1]. Show that fe R(0, 1] and find f f. %3D

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: