(15.) For functions f and g, f(g(x))= x. If f(12) 3 and f'(12)= find the equation of the tangent line to g(x) at x 3.

Q: 3. Find the equation of the tangent line to the curve f(x): at the given point (-5,5) x+4

A: Given  function

Q: 2. Determine an equation for the tangent line to f(x) = x(x² + 1)3 at x = -1.

A:

Q: 16. Find the equation of the tangent line to the curve y = e* at the point (a, f(a)) when a = In 3.

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = x ln(x…

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Q: 1. Find the equation of the tangent and normal line to the curve f(x) =x' - 3x +2 at (1, 0).

A: Given the function f(x) :

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: Consider the graph of the function f(x) = ln(1 + x²) for x > 0. 1. Find f'(x). 2. At which value of…

A: Ta which value of x the slope of tangent line the greatest.

Q: Find the equations of the tangent lines to the graph of y = ln  x  at x = 1 and x = -1.

A: To find equation of tangent lines at x=1 and x=-1f(x)=lnx

Q: 2. Find the equation of the tangent and normal line of the function y+ 3xy +x = 5 at the point (1,…

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Q: 4. Determine an equation for the tangent line to g(x) = 3 csc(x) – 2 at a = T/4.

A: Solution :-

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: 7. Find the equation of the tangent line (in the form y = mr+b) for the function f(x) = In(x-3)+6V…

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Q: 2 Find the equation of the tangent line to the graph of f(x) = at The equation of the tangent line…

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Q: 3b. Find an equation of the tangent line to f(x)=2x+x-1 at the point Where x 1. %3D

A: The solution of the problem is given in the next step.

Q: B) Find an equation of the tangent line to the curve at the given point y = (1+ Vx)³ at x =1 ?

A: Given curve is, y=(1+x3 )3 at x=1.  The objective is to find the equation of the tangent.     For…

Q: Find an equation of the tangent line to the curve at thegiven point.   y = e2x  Cosπ   x, (0. 1)

A: Given: y=e2xcosπx at 0,1 for finding equation of tangent at given we need slope m of tangent at that…

Q: 2. Find the slope of the tangent line to the curve f (x) = -1 2 at x

A: Given: f(x)=2x

Q: 7. Find an equation of the tangent line to the curve y = 1 y = 1+3r IVI that is parallel to

A: The objective is to find the equation of tangent line.

Q: 2. Use implicit differentiation to find the tangent line to the given curve at the given point P (a)…

A:

Q: 6) Find an equation of the tangent line to the graph of f (x) = 4 ln z at the point (1, 0).

A:

Q: 8. Find the equation of the tangent line to the curve y = e* at the point (a, f (a)) when a = In 3.

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Q: *4. Find the equation of the tangent line to r² – 3ry + y² = -1 at (2,1).

A: Equation of tangent at a point

Q: Find an equation of the tangent line to the curve at thegiven point.

A:

Q: 13. Find the equation of the tangent line to the curve x'y' + 4.xy = 12y at the point (2,1).

A:

Q: 4. Find the equation of the tangent line to the graph of x3-3xy+ y2 +19 =0 at the point in the…

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Q: 2 Find an equation of the tangent line to the curve y at the point(0,1). (1+e¬x)

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Q: 15 Find the equation of the tangent line to the graph of f(x) at the point where x = 2 Vx3 – x + 3

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Q: Find the equation of the tangent line to the curve tan(x – 1+ 2y) = e + 3x – 4 at the - point (1,0).

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Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

Q: d the equation of the tangent line to the graph at the specified value of x. y=x√3-x², z = 1.

A: Given query is to find the equation of the tangent.

Q: 2) Find the equation of the tangent to f(z) = 3re² when x = 1

A: A detailed solution is given below.

Q: 4. Find the equation of the tangent line of the graph of f(x) = 12/T – 16 at the point where the…

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Q: Determine the equation of the tangent line to the function g(x) = (2ex)/x at the point, (2, e2).

A:

Q: 4. Find the equation of the tangent line to the curve 2xy+r sin y = 27 at the point (1.%).

A:

Q: 4. Determine the equation of the tangent line to y = x²sin2x, at x = - R

A: Follow the procedure given below.

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: 6. Find the equation of the tangent line to f(x)= = tan (2x) at the point (n/8, 1).

A:

Q: 12) Find the equation of the line tangent to g(x) = (3x + 11)ex-4 at x = 4.

A: ddxuv=vddxu-uddxvv2

Q: 1. Given f(x) : x3 > find the equation of the tangent line when x = 2

A:

Q: 3 Find the equation of the tangent line to the curve x*y – xy = –2 at the point (-1, –1

A: Given: x4y-xy3=-2 and the points are (-1,-1)

Q: - Find an equation of the tangent line to the curve sin(r+y) = 2y – 21 at the given point (-7, –x).

A:

Q: 1. Find the equation of the tangent line to the graph of In(x + y) = 4y² + x*y at the point (2, -1).…

A: Solve the following

Q: 9) Find the equation of the tangent line to: y = (1+x) e*when x=0

A:

Q: 1. Find the equation of the tangent line to y e* at x = 0. = - x²+1

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Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value.   f(x) = x ln(x…

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Q: 12. Find the equation of the tangent line to f (x) = x³ at the point P(1,1).

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Q: 7) Find the equation of the tangent line to the graph of f(x) = –sin(x) +3 at x = 4

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e-X…

A: Given: f(x)=e-xln(x)

Q: 2 Find the equation of the tangent to the curve y = sin x at the point where x = . 3

A: