59 An Analysis of antenna radiation patterns for a system with cir- cular aperture involves the equation g(u) = [ f(r)Jo(ur)rdr %3D If f(r) = 1- r2, show that 2 g(u) = 1(u) %3D

Q: Examine the differentiability of the function f(x)=|cosx| at z 2 %3D

A: Given: f(x)=|cosx|

Q: (c) Let u(x, t) satisfy the hyperbolic system 4u, - u = 4 cos(t), xe R, t > 0. i. Find a general…

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: know that a3 .8

A: Antiderivative: F(x)=f(x9) F'(x)=f'(x9)*ddx(x9)       =f'(x9)*9x8 F'(a)=9f'(a9)a8       =9*13*6…

Q: (5) (sec-i x) =, d

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Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: Find f'co) if fco)= (Since\ %3D

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Q: (d) Calculate the coefficients (B's) by estimating separately the following models (Use the formulas…

A: The coefficients of β's can be estimated by using the method of least squares.

Q: = Use the graph and the given equations, f(x) = 5x² (red) and f(x) = to support your response to the…

A: We have to use integral to find area bounded between curves or line .

Q: Acetaminophen is a common pain reliever and fever reducer Here is a graph showing the amount of…

A: a. From the graph, it is seen that the vertical intercept is at (0,400) It implies that initially an…

Q: 1 Find an equation of the tangent line to the graph of f(x) = c) at a) at (1,1); b) at 3, '27

A: Given - A Function To find - Its tangents at given points

Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: (a) Use f(t) = a cos (b(t- c)) + d to model these conditions. (b) Evaluate f(1) and f(7). (a)…

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Q: The differential equation ty' = cos² (y) is . ...linear, separable, and autonomous. O.nonlinear,…

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Q: 1) fix) = (x-2).x+1 find the maximum,minimum and inflection paints of the finction. %3D

A: An inflection point is a point at which the second derivative is equal to zero or is undefined and…

Q: Let f(r) be a differentiable function on R. The figure below is the graph of the derivative of f(r).…

A: We can use wavy curve method : Critical point → f'(x) = 0.maxima →  when f'(x) changes sign + ve to…

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: 4 (a² - y²)² 4. g(x) = (3x² + 4x - 5)5 3. 2 =

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Q: 1) A curue with *a) = (2,4 4), 22)=(0,2,4). %3D Find K(2), B(2).

A: solution : Given α'→2=2,4,4α''→2=0,2,4find K2 & B→2=? formula of Kt=α't×α''tα't3now first we…

Q: If mZDFC = (11g 9), find g so that FC 1 FD. %3D D F

A: if two line are perpendicular then angle formed is of 90 degree

Q: Vズ+1 7.y=ューズ %D (x+1)2 Vズ+1 - 8. у %3D

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Q: d²y Find and dx then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t2 –…

A: We have to find first and second derivative for the given parametric function.

Q: I +1 is normal to the f(r) given by the implicit equation If the line y curve y %3D sin(y) + I =…

A: The slope  of a curve y = f(x) at a point  is its derivative y' at the given point

Q: 8) y = (x² + 3)ln 4x5 dy (x² + 3) · dx 2x² In 4x° + 5x² + 15 1 - 20x + In 4x³ · 2x 4x A) dy 2х + 1…

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Q: The table below shows the height (in meter) of a javelin as it is thrown and travels across a…

A: