4х + 5 f(x) 9 — Зх -

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

Q: Describe the interval(s) on which the function is continuous. f(x) = sec x/4

A: The denominator can not be 0.

Q: Find the points of discontinuity of the function f(x)=arctan1x if they exist.

A: The given function is not defined at x = 0. Now the left hand limit at x = 0 is, And the right hand…

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 < x < 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given, the function f(x, y) = 5x – 10y + y3, we have to show that the function is differential by…

Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

A:

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f(x) = 2x 2 +…

A: Given:                fx=2x2+10x,     a=3 Find: f3+h and f3 f3+h=23+h2+103+h…

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: To find two path of approach for the given function such that we conclude that no limit exist when…

Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: Find values of a and b so that the function f(x) = x + ax +b has a local minimum at the point (7, -…

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Q: The function f(x,y)=/26-2x²-y² is continuous at point (2,-3). .A False .B True

A: A function is continuous at a point if after putting the point in the function yields a positive…

Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (x) = x +…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. For a…

Q: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

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Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = 2x2 +…

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Q: By choosing x, find a maximum of xre-x, if r>2, otherwise the function goes to infinity at x=0.

A:

Q: Suppose that f(a, b) is an absolute maximum of the function f (x, y). Must f (a, b) also be a local…

A: First of all, undrstand the difference between absolute maxima and local maxima.Let, z = f(x,y)…

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

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Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

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Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Find the absolute maximum and minimum assuming the function is f(x) = 2x^4 - 8x + 3 on interval…

A: f(x)=2x4-8x+3

Q: How can you sometimes decide from examining ƒx and ƒy that a function ƒ(x, y) is differentiable?…

A:

Q: Give the three conditions that must be satisfied by a function to be continuous at a point.

A: We have to write  the three conditions that must be satisfied by a function to be continuous at a…

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: Find the largest open interval using the tools of calculus where the function is changing as…

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Q: The Bisection method is based on the principle that a continuous function which is positive at one…

A: Consider the provided question, We have find the value after third bisection process of the function…

Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

A: Given f(x,y)=x3-y2-48x+8y

Q: On what interval is the function f(x) = x^3 - 4x^2 + 5x concave upward?

A: Use given function find the required result

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 31.…

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Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

Q: Find the x-values (if any) at wvhich the function f(x)= 9x+ 3x+ 3 is not continuous. Which of the…

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Q: Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x = because…

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Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

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Q: 1 . Let f(r) 2r + 1

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Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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