a) Show that the function given by f(x) = x* + x – I has exactly one zero b in the interval What is the equation for the tangent to the graph y = f(x) in the point (-2, f(-2))? Find the intersection petween the x-axis and the tangent. Find an approximation to the zero b by using Newton-Raphson's method with one iteration and initial guess Co = -2. ) Explain briefly why Newton-Raphson's methode (for the function given by f(x) = x* + x – 1 which has exactly one zero b in the inteval (-2, –1)) with initial guess xo =-2 gives a sequence xo, x1, x2, ... with co < x1 < x2 < x3 < • · · < xn < xn+1 <…….< b. The argument should mention both the first and second derivative and there should be a clear illustration explaining your reasoning.

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: a) Find 2 x-intercepts of the function f (x) = a² + 6x . The x-intercepts are and (write smaller…

A: a) The x-intercepts of a function is the points where the graph crosses x-axis . The values of y…

Q: Find the equation of the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

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Q: Find all values of x for which the tangent line of f(x) x2 + 18x + 96 is horizontal.

A: fx=x2+18x+96 Differentiating with respect to x, we get f'x=ddxx2+18x+96=12x2+18x+96·dx2+18x+96dx…

Q: For a function g, we are given that g(-6) = -8 and g'(-6) = 3. What's the equation of the tangent…

A: For a function , we are given that  and .To find the equation of the tangent line to the graph of…

Q: find an explicit formula for f' and use it to graph f' f and the line y=x on the same Screen. To…

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Q: Determine the equation of the tangent line of the given function: f(x) = 3x² – 2x; (-1,5) y = -8x-3…

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Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x' +4x +1

A: f(x) = x5 + 4x + 1 Basic formula for Newton's Method is: xn+1 = xn - fxnf'xn f'x = 5x4 + 41 + 0 =…

Q: Find the equation of a tangent line to the graph of f(x) = x² – 2X at (-2,8). TYPE IN THE EQUATION…

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Q: The slope of the tangent line at any point (x, y) on the curve 3x2 -2x+7 and the point (1, 3) is on…

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Q: Find the value of C' for which the tangent line to the graph of the function f(x) = 2e at the point…

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Q: Apply Parseval’s formula to the function f(x)=x2.

A: As per the question we have the function f(x) = x2 and we have to apply Parseval's formula to this…

Q: 3- Find the root of function F(x) = x² – 10 Using XL=3 , X,-4 , ɛ = 0.1

A: given function Fx=x2-10 with condition XL=3, Xu=4, εS=0.1 claim- find the roots of the function

Q: Determine whether the pairs of the functions are linearly inde- pendent or linearly dependent on the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: 3a) Determine the equation of the tangent to f(x) = In(3x + 4), at x = 2. %3D Equation of Tangent:…

A: Please see the explanation below

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.