30 Find the real and imaginary parts of the functions (a) z²e2= (b) sin 2z Verify that they are analytic and find their derivatives.

Q: Complete the differentiation formulas a) d/dx(c)= b) d/dx(ax+b)= c) d/dx(x^n)= d) d/dx(1/x)= d)…

A: We have to find derivative

Q: Find The derivative of The functiin' toy do not nud to Simpliy The answer' y= arcscc (In 69) +…

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Q: The method of u-substitution is the integral analog of the chain rule of derivatives and the method…

A: Let say we have two functions f(x) & g(x)Now combine the function f(g(x))Hence, the derivative…

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Find an equation of the tangent line to the graph of the function f(x) = tan2(x) at the point

A: topic - equation of tangent line to curve

Q: Y^5+X^3=Y^2+9x,Tangent At (0,1); Find The Equation Of The

A: We have to find the equation of the tangent of the curve y5+x3=y2+9x at (0, 1).

Q: Find the average rate of change of the function f(x)=x^3over the interval [1,1+h]. Simplify your…

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Q: Let /= (-00, 1] and let f(x) =V1-x for x E I. Let G = (-e, e). One of the following open intervals H…

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Q: /3 store the functian fCx) = (2.7x³-37+5) in your graphing utility. Usethe numeric differentiation…

A: Given: fx=2.7x3-3x+523 To Find: i. f'0 and f'4.3ii. Graph fxiii. Number of Horizontal Tangents

Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

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Q: For gxy=0, shouldn't that be -12 instead of 0? Because since gx = 3x^2-12y, when you do the mixed…

A: Let                       For critical points we have          Consider…

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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Q: What are the indeterminate forms and L'hospital's rule in application of derivatives?

A: We have to define Indeterminate form and L'Hospital Rule

Q: Fill in the appropriate blanks for the derivatives of the given functions, then evaluate each…

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Q: Verify Cauchy-Riemann equation for the function f(z) = z^3

A: To find- Verify Cauchy-Riemann equation for the function fz = z3         Formula Used-…

Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

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Q: How do the two versions of Fundamental Theorems of Calculus enable us to understand further…

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