If w = f(z) is analytic function, %3D under what condition z = g(w) is ?analytic function too

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Determine analytically the point (s) at which the graph of the function has a horizontal tangent. x2…

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Q: the derivative of E(q) is-(q*(q^2-1))^-1. what's its global maximum and global minimum. Thank you!

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Q: Use the definition of derivative to find f'(x) for f(x) = ax² + 10. f(x+h)– f(x) | f'(x) = lim h0 h

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Q: 2. Use the definition of derivative to find the derivative for f(x) = x2 + 3x . | f(x +h) – f(x) lim…

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Q: 5. Use the definition of the derivative to find f'(x) if f(x)== x-÷ (i.e. ƒ(x)= . (i.e. f(x +h)-…

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Q: B)Is w = Ze² analytical function or not?

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Q: The definition of the first derivative of a function f(x) is: Select one: f(x+Ax)-f(x) a. f'(x) =…

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Q: if f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable at (2,F(2))   true…

A: Given statement is If f(x) is a function that is continous at (2,f(x)) then f(x) is differentiable…

Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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

A: Answer

Q: Consider the function y = coth(x + 1). Which one is a critical number of this function?

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Q: Step 1 Apply the Definition of Tangent Line with slope m, f(e + Ax) - (c) lim Ax - -6 Ax to the…

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Q: .Find the Global Extrema for f(x) = Bx4-BeB-A)x. Use the second derivative to determine if those…

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Q: Can anything be said about the graph of a function y = ƒ(x) that has a continuous second derivative…

A: given

Q: 1. Below is the graph of f(x) = |x]. Using the left side of the function with the equation y = – x,…

A: The graph of fx=x is given. The equation for the left side of the graph is y=-x and the equation…

Q: 1. Below is the graph of f(x) = |x]. Using the left side of the function with the equation y = – x,…

A: The graph of f(x)=x is given

Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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Q: Let y = f(x) be a differentiable function. If the derivative of f is zero at x = a, then the…

A: Given statement : Let y=f(x) be a differentiable function. If the derivative of f is zero at x=a,…

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

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Q: Two business students at Brock University decided to open a small company together to sell their own…

A: Given query is to find the the correct option for rthe graph of f(x).

Q: B)Is w = Zez analytical function or not?

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Q: Find the imaginary part of an analytic function whose real part is e* (xcosy - ysiny).

A: it will be satisfy CR law equations

Q: Starting from the definition of derivative prove that if f(x) = 1 then f'(a) = a2

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Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

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Q: Let y = 5−2x be the tangent line to a function y = f(x) at x = 3 and y = 2+3x is the tangent line to…

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Q: belov are four types of functions. VWnich does not possess a derivative of the same type? a)…

A: To find which function does not possess a derivative of the same type?

Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

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Q: The graph of a function is shown together with the tangent line at a point P. 10 9. 8. 7 6. 4. 3 2 1…

A: Here from Graph Red line tangent to given function f at point p  so derivative of f is equal to…

Q: Let f and g be the functions defined for x > 0 by f(x) = (Væ)* and g(x) = (Vx)** Which function is…

A: According to the given information, Consider the function f and g defined as:

Q: Two business students at Brock University decided to open a small company together to sell their own…

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Q: Determine whether the function 1s differentiable. at, X=1$ then sketch a graph of ysf (x).

A: Step:-1 Given that fx = xif x≠12if x=1 And Right , left derivatives are respectively,   f+' 1…

Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Suppose the only information we have about a function fis that f(1)=2 and the graph of its…

A: Ti find the linear approximation.

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: find a linearization at a suitably chosen integer near a.

Q: The function defined by x2 if r 0 is continuous at a = 0. Determine the left- and right-hand…

A: We have to check our function is differentiable at x=0 or not

Q: It costs Sugarco 25¢/lb to purchase the first 100 lb ofsugar, 20¢/lb to purchase the next 100 lb,…

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Q: Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion.

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Q: The graph of the derivative of a function f is given. According to the graph, f has a local minimum…

A: We know that local minima and maxima exist at critical points (where function is not defined or it's…

Q: Suppose fis a function whose derivative is given by f'(x) = following statements are true?…

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Q: Let f be a function with first derivative given by f' (x) = (x + 1)(x – 2)(x – 3). At what values of…

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Q: Let f(x) be the function defined below. f (x) = Vx + 3 Use the limit definition of the derivative to…

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Q: Sketch the graph of a twice-differentiable function y = f(x) that passes through the points (-2, 2),…

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Q: Let g be a function that has derivative x(x – 3) (x – 5)e2" g'(x) = Does x=3 belong to a local…

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Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: Find the linearizationsof the following functions at x = 0. tan x

A: Linearization is tangent line at a point x=atangent equationy-y0=mx-x0m=f'a

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.