Q3) State the approximation for a differentiable function f(x): (a) V51 (b) V123 (c) (33)

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: How is linear approximation used to approximate the value of afunction ƒ near a point at which ƒ and…

A:

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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Q: what is the largest vertical distance between the graphs of the functions y=x^1/2 and y=x^2 in the…

A: To find the largest vertical distance between the graphs in the interval given

Q: The graph of f(z) = 2z³ + 12z² – 126z + 17 has two horizontal tangents. One occurs at a negative…

A: for the horizontal line find the slope first and set to zero.

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

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Q: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]?

A: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]

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: Solve for the slope of the functions at the points specified using the limit definition of slope of…

A: Consider the function  f(x) = 12x2− 9x + 15 point (−2, 81).

Q: Lat f be a continous and differentiable function. If f'(c) = 0 then c is a local maximum or local…

A: Answer

Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to…

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Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

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Q: 15. Differentiate using quotient rule: x+2 y = х-2

A: Given, y=(x+2)/(x-2) Then,dy/dx will be

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: Use the second derivative test todetermine whether f(x)--+ 18z has a localmaximum or localminimum at…

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

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

A:

Q: Find the slope of line drawn tangent to the function. f(x)=x2+7, at the point (-2,11) by using the…

A: Shape of tangent line to the curve is given by first derivative of curve at given periodDerivative…

Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: Find the interval on which the curve y = - -∞, 6 dt is concave upward. (Enter your answer using…

A: We have to find out

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: The slope of the tangent line to the differentiable function f at the point (2, f(2)) is…

A: It is given that the slope of the tangent line to the differentiable function f at the point 2,f2 is…

Q: Use the linear approximation to estimate Af = f(3.2) – f(3) for f(x) = 1+x² * (Use decimal notation.…

A: Given: f(x)=81+x2

Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

A:

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: Use Secant Method to calculate the root of a function f(x) = e-*(3.2sinx – 0.5cosx) on the interval…

A: To use decant method to calculate the root of a function

Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

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Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

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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: Let f (2) = (4z + 3) (i – 2). What is the real part of the derivative f' (1+ i)?

A: A complex-valued function consists of two parts. The part without i is referred to as the real part.…

Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

A:

Q: Find a point 2o where the function f (2) = (z – 12 – 12i) (z – 12 – 12i)differentiable. What is the…

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

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

A:

Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, ¤]?

A:

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

A:

Q: Let f be the function given by ƒ(z)=2z + 3z² +1. What is the absolute maximum value of f on the…

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Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Find the equation of the tangent to the curve y = 2x² – 1 at the point where z =1. Use the limit…

A: We know the standard form of tangent line is     --->     (y-y0) = m (x-x0)   where 'm' is the…