Consider the piecewise-defined function f defined by S7 – 4x² if x > 1 f(x) %3D 11 8x if x < 1 Find f'(1). If ƒ is not differentiable at the number c = 1, enter DNE. f'(1) =

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

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Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: Let y=x2+2x. Compute Δy and dy at x=3 if dx=0.2. What is the difference between Δy and dy? That is,…

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Q: A point is moving along the graph of the function y= such that dx/dt = 4 centimeters per second.…

A: derivative

Q: Suppose y = (x + 1)5, and both a and y are functions of t. If. dy :1, find dt dx when x = = 1. |3D…

A: Given data:   The given function is y=(x+1)5. The first value given is dy/dt=1. The given value of x…

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: Using a local linear approximation of f(x) = v4 + x at a 0 to estimate the value of v4.3 gives

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Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

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Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. dy…

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Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x = 4. dy…

A: Consider  y=2x+1 where x and y are function of t.

Q: ²+ re" = 2y + e² %3D

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Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

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Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: Use Euler's method to make the graph of the following functions on the given interval. a) dx/dt = t…

A: Introduction: The Euler's method is a basic and numerical method to approximate an initial value…

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 6, find dt dy when x = 4. dt (a) If dy…

A: Given y=2x+1 dydx=dydtdxdt

Q: Consider an F-curve with df = (15, 5). Determine the F-value that has area a. 0.025 to its left. b.…

A: a).  Procedure to obtain F-value using MINITAB software is given below: Choose Graph &gt;…

Q: Find the equation of the tangent line for f(x) = 6 tan(x) at a = %3D a) Oy = 6/3 (z -) + + 12 b) Oy…

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Q: If y = x - 4x and x = V2r + 1, find dy/dt when t = 1= V2.

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: if x 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

A: To find f is differentiable at 0 or not

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: Find the si0pe of the given Function メト at メ= y' 1.) u= Vler*) at x = 2) 4= In(3メ-2) a+ x= こ %3D

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Q: Find a continuous solution satisfying dy dx + 2xy = f(x) where { x if 0 < x < 1 romer 0 if x ≥ 1 ,…

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Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

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Q: Let y = f(x), where   f(x) = 4x2 + 6.   Find the differential of the function.   dy =?

A: Given: y=fx=4x2+6 now differentiating given function with respect to x

Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: Q4/ Find the direction in which the function f(x,y) = xy2 +1 increases most rapidly at P-(1, -1) and…

A: We have to find the direction in which the function fx,y=xy2+1 increase most rapidly at P1,-1 and…

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: S() dt, where f is a continuous function, find f(4). (c) A 10 ft ladder rests against a vertical…

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Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: Q1) x x = %3D 1+1 4) Area between t-2 to t-5. 5) Length of the curve between t2 to 3.

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Q: Suppose y = /2x + 1 , where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. (b)…

A: Differentiating with respect to t, we get

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy…

A: we will diferenciate the equation of y with respect to t, and solve this.

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: Find the particular anti derivative that Satisfies the following conditions dy 4x +3 ; y(1) = 8 dx…

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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.