Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval. y = sin(x3),  (1, 2)

Q: Find an equation of the tangent line to the graph of f at the given point   f(x)=(2x+1)/(x+2),…

A: Given  fx=2x+1x+2 To find tangent differentiate the function f'x=x+22-2x+1.1x+22     =2x+4-2x-1x+22…

Q: Find the equation of the line tangent to the graph of f(x) = -3 cos (x) at x 2

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Q: The derivative of the function f is defined by - f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what…

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Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

A: Given   y = sin (x3) ....(1)   , (1, 2)

Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

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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: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: Find an equation of the tangent line to the graph of the function at the given point.

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Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: 17.) Find one point P on the graph of f(x) = x² such that the tangent line to the graph of f at P…

A: To find a point P on the graph of fx=x2 such that the tangent line to the graph of f at P also…

Q: Find an equation of the tangent line to the graph of f(x) = x^4 + 3x^2 -1 at x=1

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Q: Find an equation of the tangent line to the graph of f at the given point.         f(x) = (x − 4)(x2…

A: Given, The function, f(x) = (x − 4)(x2 + 6x − 1).

Q: Find an equation of the tangent line of f at the given point, f(x) = (x+2)(x² +5), (–1,6)

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Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = sin x − 1, 0…

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Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: 5x f(x)= x²-2

A: We have to find the equation of tangent line of the given function. So first of all we will find…

Q: 3. Find the equation of the tangent line to the graph of f (x) =7-3x-x at x= 1 %3D

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Q: For what values of x in [0,2pi] does the graph of f(x)= x + 2sin(x) have a horizontal tangent?

A: Horizontal tangent:The slope of a tangent of the graph of a function f (x) is df (x) ∕dx. For a…

Q: Find an equation of the tangent line to the graph of the following function f at the specified…

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Q: Show that the graph of the function f(x) = 3x + sin x + 2 does not have a horizontal tangent line.

A: Given: fx=3x+sinx+2 we know that for horizontal tangent slope of tangent has to be zero and slope m…

Q: Find the equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

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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: Find an equation of the tangent line to the graph of f at the point  (2, f(2)). f(x) = 3(6x − 2)4…

A: The given function is f(x) = 3(6x-2)4The slope m is obtained.

Q: Find the equation of the tangent line to the graph of f(x)= 1 at the point (2,1). %3D X-1

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Q: Find an equation of the tangent line to the graph of the function f(x) = x² In x when x = 1

A: Given: f(x)=x2lnxx=1

Q: 2. Find all points at which the tangent line is horizontal on the graph of the function f (x) = 2x3…

A: The slope of any horizontal line is 0. and the slope of any function is just its first derivative.…

Q: The equation of the tangent line for the function f(x) = -3 – 6x at r = 6 is %3D

A: The given function is, fx=-3-6x We need to find the equation of the tangent line to the function at…

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 3x2 - 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) =  3x…

A: Point of tangency = (2, 8)m = slope of the tangent line = f'(x) at the point of tangency =…

Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

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Q: Find an equation of the tangent line to the graph of the function F(x) = tan²(x) at the point 1 -4x…

A: Here we find the tangent equation.

Q: Find an equation of the tangent line to the graph of the given function at the specified point. x² –…

A: We have to find the equation of the tangent line

Q: 3. Given that the graph of f passes through the point (2,5) and that the slope of the tangent line…

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Q: If f (x) = sin 2x , find all of the stationary points of f (x) on 0<x<2n

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Q: 3 y = In(3 + x) + 3+x' (-2, 3)

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Q: Find the Equation of the tangent line of "f" at the given point. f(x)=(x-4)(x2+6x-1),(0,4)

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Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

A: Plot the graph of sinx given below

Q: Find the equation of the tangent line to the graph of the function f(x): = x+7 x-8 at the point (0,…

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Q: Find the equation of the tangent line of the function at the given point. 9. f(x) = 3x+2 (0,-2) x-1…

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Q: Find an equation of the tangent line to the graph of f at the given point. x + 2 1 -5 2 f(x) X - 1 y…

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Q: Find the slope of the tangent line to the graph of f(x) at the point (1,2). The function is…

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 –…

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Q: Find the equation of the tangent line to the graph of the function f(x)=(x2+8)(x−3) at the point…

A: Given: y=fx=x2+8x-3 at 0,-24 we know that for finding equation of tangent we need to find slopem of…

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: 1. Find the equation of the tangent line to f(x)= 4x2 - 5x+2 at (-1,11).

A: We can find the equation of tangent to the curve as below.

Q: Find equations of the two tangent lines to the graph of f that pass through the indicated point.…

A: Given function is fx=4x-x2. To find the equations of the two tangent lines to the graph of function…

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

A: Given- fx=x+2x2+5 To find- An equation of the tangent line to the graph of f at the point -1,6…

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.