J 9x? x > 0 x < 0 Let f(x) (d) Is ƒ'continuous on R? Use the definition from 6.1.1 lim(x → c)2 )f(x) – f(c) х — с

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

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Q: 1. Define a function f as follows: | x² + 1 if x 0 4 -3 -2 -1 1 3 The graph of f. (a) Use the limit…

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Q: Consider the function below. (x, y) = x²e^xy (a) Evaluate f(3, 0). (b) Find the domain of f. ORX (0,…

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Q: Show that f(xr) is continuous but not differentiable at the indicated point. Sketch the graph of f.…

A: Consider the functions  a)fx=x3,                     x=0b)fx=x−223 ,           x=2

Q: Q2. Show limit DNE зеуг 101n(x) lim (x,y) → (0,10)

A: Q2 asked and answered.

Q: du u (х, 0) — и(0,0) lim x→0 %| да (0,0)

A: Consider a function f(z)=u(x,y)+iv(x,y) such that     z=x+iy∆z=∆x+i∆y If the function is…

Q: pose that the function f is continuous everywhere. Suppose that F is any antiderivative of f, and…

A: In this question, the concept of Integral is applied. Integration Integration is a method of…

Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x&lt;1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: (H.W): Is this function

A: We have to check whether g:R--&gt;R ,g(x)=x^2 subjective or not

Q: lim b→∞ 2x 22 x² + 1 -b dx.

A: To solve the following problem of integral and then find the limit

Q: Consider the function given by z-y+2/7–2/9 se r+ y, x>0, y> 0 f(r, y) = k(x), se ¤ = Y n the…

A: function is continuous

Q: Prove that for any function f : X → Y and for any subsets Y₁ and Y₂ of Y, ƒ¯¹(Y₁ NY₂) = ƒ¯¹(Y₁) Ñ…

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Q: Stample? bet ftz)= if Show that a)f(2)is Continuous everyulhere on- 7 the Comptex derivative fo)…

A: Like a real-valued function, a complex-valued function can also be continuous and differentiable. A…

Q: Let f be a differentiable function such that f(h) f(x + y) = f(x) + f(y) + 2xy and lim = 15. Find…

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Q: 3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

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Q: LO KB allla the domain of f (x) = x²-4 is: x-1 [-2, 1) U [2, 00) O (-0, -2] U [2, 0)O [-2, 1) O [2,…

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Q: Suppose that f is differentiable on R and f'(x) = e*-4x+3 – 1 for all x E R. Determine all intervals…

A: Find your answer below

Q: Let the function f(x) be given as follows: ax + b, x<1 f(x) = ; lt +x + 1, x 21 Employ appropriate…

A: is differentiable. Therefore, we have, RHD=LHD=f(x) Now,

Q: Consider the function f(r, y) = 212 + ry – 6ry + 5x +2. (a) Show that (1,3) is a stationary point of…

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Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given