Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.
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Q: For numbers 21-23, consider g(x) = 5x² - 2√x³ 21. Which of the following shows the domain of g(x)?…
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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.
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Q: Prove that (r) = tan(r) is uever negative in 0 <r< and show that g(x) = xsinr decreases…
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Q: Let f(x,y) = x - 2xy – y“. Compute f(3,0) and f(3, – 7).
A: To compute f(3,-7) Given:- f(x,y)=x2-2xy-y2
Q: a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 +…
A: The first step inludes the partial differentiation of the functions individually with respect to y…
Q: Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x;)…
A: Solution: (1) f''xi=fxi-2fxi-1+fxi-2∆x2 We know that f'xi=fxi-fxi-1∆x ......(1) Then,…
Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.
A: We have to prove given identity: Concept:
Q: Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2] 1.a O V8 b 0 3.cO 8 dO
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Q: If A(x) = f(t)dt is increasing on [0,10], then f(x) must be increasing on [O,10]. True False
A: Given
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: Prove that f(x) = [[sin²(2log r)– 3 sin ( 2logt)+2] dt %D 1. Cannot be decreasing any where,
A: To prove that f(x) can not be decreasing anywhere, where f(x) is defined as…
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: 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: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE
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Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.
A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.
Q: Let f(x) = ri- 2xi.Find the value of c that satisfies the conclusion of Rolle's Theorem forf on (0,…
A: The graph is shown below:
Q: {(u)= (u² -3)*
A: Given the function is f(u) = 12u2-32. We have to find f'(u).
Q: 1 Let f (x) = ; 1 , then f (x) satisfies the - - 2 conclusion of Rolle's Theorem on 0, 1| 6.
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Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…
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Q: b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D 2- f(x,y) = Inx2 + y2…
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Q: let f(x) = { ax2+x+1 if x is less than or equal to 1 { bx if x >1 find a and b…
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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<0 So,…
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: Can Rolle's Theorem be applied to f(x) = 1/(1-x) on interval [0,3]? If yes, what is c in (0,3) such…
A: here we can't apply the rolles Theorem
Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…
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Q: X if x e Q If f (x) is defined on [0,1] by the rule f (x) = < (1-x , if x 4 Q Prove that fof (x) = x…
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Q: 5. Use Green's Theorem to evaluate f. $ (y² – 4x) dæ – (2+ x²y²) dy where C - - is shown below. y…
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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).
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Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition F(4)= 0? A,…
A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.
Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…
A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…
Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…
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Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].
A: Here given
Q: Let F(x)=∫(from −4 to x) −2cos(t^2)dt. Use the Fundamental Theorem of Calculus to find F′(x).
A: Solution:
Q: Q3: a) Let f : Z → Z be such that f(x) = Vx² – x + 1. If invertible, and if it is, what is its -…
A: the function is invertible if its one -one and onto. The function is one - one if f(x1)=f(x2)…
Q: Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2] .a 3 .b 8 .C 8, .d 1
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Q: 1 dt, for x > 4. In(t) Let F(x) 4
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Q: | Are fi(x) = x and f2(x) = x² orthogonal on [-2, 2] inter- val? Find c and c2 so that f3(x) =…
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Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)
A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…
Q: 1. Use the definition of the derivative of complex function to show that f(z) is not differentiable…
A: We will show the given statement.
Q: 15. If f+g is differentiable at a, are f and g necessarily differentiable at a ? If f g and f are…
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Q: 2. Use the Intermediate Value Theorem to prove that the equation e* = 4 - x³is solvable on the…
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Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…
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Q: 1. If f(x) = x + v2 – x and g(u) = u + /2 - u, is it true that f = g?
A: Since you have asked multiple questions in single request so we will be answering only first…
Q: Let f(x) = x² In x, where x > 0. Show that f(x) has only one critical point.
A: Given data: The given function is f(x)=x2lnx. The critical point is the point where the slope of the…
Q: Let S(x²+2x)², x> 1, f(x) = Tax+ bx², ах x< 1. Compute for all a and b such that the function f(x)…
A: Proceed as shown
Q: Let f be the function from R to R with f (x) = x2. Is f invertible?
A:
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- Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘ ƒ)(x) = | x2| = x2 are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the Chain Rule? Explain.State why the function 2z2 - 3z + e-z is analytic everywhere.we have f: X→Y is a 1-1 function and Y is countable. Since f is 1-1, is it correct that this implies X ~ f(X) [which is f:X →f(X)] which further implies bijecton? Also, does this imply f(X) ⊆ Y?
- Let the function f:R-->R be twice differentiable and suppose that f(x)≤0 and f''(x)≥0 for all x. Prove that f:R-->R is constant.Suppose F 1 and F 2 are both antiderivatives of f on an interval I How are F 1 and F 2 related?Suppose that the function f: [0, 1] in R is continuous and thatf(x) > 2 if 0<=X < 1.Is it necessarily the case that f ( 1) > 2?