3) Show that the function 13-212+2 g(2) = is a Complex differontiable function ait the point 20 =1 the comple x derivative 9'2).

Q: Find the equation of the tangent line of y = 6e* at xo = 0. (Use symbolic notation and fractions…

A: The given function is y=6ex, to find the equation of tangent at the point x0=0

Q: If cosh x  =5/3 and x>0 , find the values of the other hyperbolicfunctions at x .

A: Given  cosh x  =53 , x>0

Q: Find the equation of the tangent line to f (x) = ex at x = 2. Give answer in exact form. x²-1

A: Given : fx=exx2-1

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: Determine the equation of the curve whose tangent line at any point (x, y) is ex - sin x and passess…

A:

Q: 1. Use implicit differentiation to find an equation of the tangent line to the hyperbola - * = 1 at…

A:

Q: If tanh x = 12/13  find the values of the other hyperbolic functions at x

A:

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: 8. Find the point of the graph of f (x) = xe-2x where the tangent line is horizontal. %3D

A:

Q: 8. Find the slope-intercept equation of the tangent line to f(x) = 3x² – 4x + 5 at the point (1, 4).…

A:

Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

A:

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+2…

A:

Q: do you agree that cubic function must have at least 1 x - intercept but not more than 3 whereas…

A:

Q: 9. Find equation of the tangent line to the graph of x* +y+xy' = 3 %3D at the point (1,-2)

A:

Q: sin(7x) + sin2(7x),  (0, 0

A:

Q: Find the equation of the tangent line to sin^-1 (x - 2y) = 2xy - 1 at point (1, 1/2).

A:

Q: f (z) = sin (3,/7) at the point 72,0)

A:

Q: Find the slope of the tangent line to the curve 2 sin(z) + 5 cos(y) – 4 sin(z) cos(y) + z = 7m at…

A:

Q: Find the points on the interval [0, 2π) where the graph of the function  f(x) = 2 sin(x) + sin2(x)…

A: Given:f(x)=2sin(x)+sin2(x),       [0,2π)

Q: 5. Find the equation of the tangent plane of sin(xyz) = x + 2 y + 3z at the point (2, -1, 0).

A: We have given the surface X,Y,Z at the point (2,-1,0). We have to find the equation of the tangent…

Q: Construct a cubic spline that interpolates sin x at nodes 0, T/2, T, 37/2, 27 (use the true…

A: The given function is fx=sinx and the given node points are x=0,π2,π,3π2,2π. Therefore the given…

Q: 3. Find the tangent line equation for the given function at the given point: = 3.xy at (3/2,3/2).

A:

Q: 3. Find the equations of the tangent and normal lines to the curve f(x) = /2* +cos(x*) at(0,/2).…

A:

Q: Find the equation of the tangent line of y = 4e* at xo = 0. (Use symbolic notation and fractions…

A: y=4exSubstitute x=0y=4e0=4The point is (0,4)

Q: The slope of the tangent line of the graph of the equation xy2-3x² - 2y=-3 at the point (1, 2) is a)…

A: The given equation is xy2-3x2-2y=-3. The objective is to calculate the slope of the tangent line of…

Q: omplex derivative of (Log z)^3

A: Given: log z3 To find: The complex derivative of given function.

Q: Find an equation of the tangent line to the curve at the given point. y = 8ex cos(x), (0,8) y =…

A: Here y is given find.slope.from.it then solve as below

Q: 6. Find the equation of the tangent line to the parabola y 2.x2 – x + 3 at x = 2. %3D -

A: Equation of given parabola is, y = 2x2 - x + 3

Q: Find the slope of the tangent line to the curve 5 sin(æ) + 3 cos(y) – 4 sin(x) cos(y) + x = 7n at…

A:

Q: 5. Find the slope of the tangent line to the graph of r = 2-2 cos 0 when 0

A: Given equation of the curve - r = 2-2cosθSlope of the tangent to the curve is given by drdθ,drdθ =…

Q: 2) Find all points on the graph of f (x) = 2 sin x + sin2 x at which the tangent line is horizontal.

A: Given fx=2sinx+sin2x To find points:

Q: Find the equation – in any convenient form – of the tangent plane to z = x² sin(x+2y) at the point…

A:

Q: The slope of the tangent line of the graph of the equation xy2 - 3x² - 2y=-3 at the point (1, 2) is…

A:

Q: Find the equations of tangent lines from S = 0 from the point A(0,0)

A:

Q: find the derivatives complex funcation. {tanh¬'(iz +2)}-1,

A: fz=tanh-1iz+2-1=1tanh-1iz+2 It is known that tanh-1x=11-x2 so it follows:…

Q: Find an equation of the tangent line to the curve at each given point. x = 2 – 3 cos 0, y = 3 + 2…

A: Topic :- Application of Derivative

Q: Find an equation of the tangent line to the curve at the given point. y = sin(4x) + sin2(4x), (0, 0)

A: general equation of line is:             y = m(x) + c where, m = slope of line    and, c = constant

Q: Find the equation of the tangent line at the given point on the curve. 3y-x = 8, (16,2) %3D

A:

Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x =a. 2- Find the…

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Q: 7. Find all x-coordinates where the tangent line to y = f(x) = sin(2x) – cos?(2x) is horizontal. -

A:

Q: 1- Find the equation of the tangent to the 2(x2 + y²)2 = 25(x² - y?) at (3,1) %3D

A: According to guidelines we should have been able to do only one question at a time #1

Q: Find the equation of the tangent line to the curve: sin (2x + y) + cos-'(x +2y) 6 at the point Enter…

A:

Q: 7-The tangent of the curve x^2+y^2- 2XY3D0 at the point (1,1), is *

A: Given,           The curve is x2+y2-2xy=0 at the point 1,1.

Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the slope of the tangent line to the curve  5 sin(x) + 2 cos (y) - 5 sin(x) cos(y) + x =5π at…

A:

Q: Find an equation of the tangent line to the curve at the given point. y = In(x² - 3xt 1), (3, 0) y…

A:

Q: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: