f(2) dz. (a) For the function f(x) graphed in Figure 5.82, evaluate 4 f(x) 2 3 4 f(2) dz Figure 5.82: Estimate

Q: Integrate f(x) from x = 2 to 8 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Gauss legendre quadrature gives the result of integration over a symmetrical limit of variavle x…

Q: find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln x

A: Consider: y=x-ln x. Find the inflection points and concavity of function. First find the domain of…

Q: The function f(x) is defined by f(x) =2. What points (x, y) on the graph of f(x) have the property…

A:

Q: The tangent to the function, f(x) = -2x² + 3 at the point (-1, 1) is the hypotenuse of right…

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Q: Find a function f such that f (x) = 2x3 and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A: Key point used: The slope m, of the tangent to f(x) at point h,k, is equal to f'x=h. Given:Eq of…

Q: 2. Find the derivative and the analytic domain of f(2) = 1+ %3D 22+1

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Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(r) = /5I+1. %3D

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Q: Sketch the graph of f(x) = sin¬'(x² + y²) by analyzing its level curves.

A:

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A:

Q: use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to…

A:

Q: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: Find a function f such that f'(x) = 2x³ and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: Consider the function f(x) = x2 - 1. (a) Find f '(x) using the limit defination of the derivative.…

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Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: am having trouble finding the equation of the line tangent to the graph of f at (1,1), where f is…

A:

Q: d) For the function {: 1- a², x2, 0 1 i) Sketch the graph of f(x) ii) For what values of r, the…

A: follow next step

Q: х — 7 - f(x) = %3D 5х + 7 Find an equation for the tangent line to the graph of f at x = 3.

A: Given: fx=x-75x+7 To find the tangent line, we find the slope Therefore differentiate with respect…

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

A:

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Given f(x)=5000+24563x-7418x2+768x3-31x4+0.14x5 Let I=∫010f(x)dx Here a=0 and b=10

Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A: Given f(x)=sinx4         , 0, 8π

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

A:

Q: Find a function f such that f'(x) = x4 and the line 2x - y = 3 is tangent to the graph of f.

A: Given that

Q: 8. 4 2

A: In this question we will use basic of calculus i.e use of tangent function. We will write the…

Q: Use Secant Method to calculate the root of a function f(x) = e-*(3.2sinx – 0.5cosx) on the interval…

A: To use decant method to calculate the root of a function

Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

A:

Q: Q2: (20 mark) a) Differentiate the function f(x) = tanx -1 secx

A: We can solve this problem using quatiant rule of derivative.

Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin…

A: Given- fx=sinx4,0,8...........(1) As we know that inflection point is a point on the graph at which…

Q: he tangent line to y= f(x) at (-7, -6) passes through the point (-9, -2). Compute the following.  a)…

A: GIVEN DATA : Equation y=fx                         Tangent of the y=fx at -7,-6 passes through the…

Q: Let f(x) = 9 – x² The slope of the tangent line to the graph of f(x) at the point (-3,0) is The…

A:

Q: 3. Find f'(x) using the definition of the derivative. a) f(x) = 7 lim f'(x) = b) f(x) = 3x %3D

A:

Q: 3. Consider the function 8x f(x) = + 15. - The tangent line to the graph of f at the point (6, f(6))…

A:

Q: Consider the function f(x) = 9x² +3. Its tangent line at x = 6 goes through the points (1, y1) and…

A:

Q: sketch the curve f(x)= ln((x^2-4)/(x^2-3x-4))

A: given curve is                                                     f(x)=lnx2-4x2-3x-4 we have to…

Q: The graph of f (x) = ax+b x²+3x-8 has horizontal tangent at (2, -1). Determine the values of a and…

A: Given query is to find the value of a and b.

Q: Consider the function f(x) = 9x + 3. Its tangent line at x = 6 goes through the points (1, y1) and…

A:

Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: On the graph of f ( x ) = sec ( x ) and the interval ( -2π, 0 ], for what value(s) of x does f ( x )…

A: f(x) = 1 on, (-2π, 0] Implies, sec(x) = 1 on (-2π, 0] i.e. x = 0 on (-2π, 0] So, x = 0  The graph of…

Q: * The tangent line to y = f(x) at (-4, 10) passes through the point (-5,-10). Compute the following.…

A:

Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a