Consider the piecewise-defined function f defined by S 7– 2x? if x >1 f(x) = 19 – 4x if x < 1 Find f'(1). If ƒ is not differentiable at the number e = 1, enter DNE. f'(1) =

Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dt…

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Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

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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: Suppose that f(x) has a continuous derivative, (T/2 f(-т/2) — 0, f(T/2) = T/4 and dx = 3. %3D 7/2…

A: Given that:

Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: Q2: Find dyidx for the following function:- (1) y = In(x + 4)-xtan (4) y =x*+1) (2) xy + x*y = x +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

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Q: Let L{f(t)} = F(s) and a ER be a constant. Which of the follo- 32- wings is wrong? ON L{f"(t)} =…

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Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: Given:         8y3+x2=1dxdt=2x=3y=-1 Differentiate 8y3+x2=1 with respect to t,…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: 1. Suppose f(x) = S*,t cos (e) dt. Find f'(x) COS 1+t2

A: We have to find f'x for the function: fx=∫-7xtcos11+t2dt This type of derivatives would be solved by…

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

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Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

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Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

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Q: Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.19). L(x) =…

A: Here f(x)=lnx at x=1We have to find the linear approximation of f(x) andAlso find the value…

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

A: By differentiating we solve the function

Q: dy for the following implicit function at p(1,1) Find dx Vxy +1 = y is O 1 O 1/2 O -1/2

A: A detailed solution is given below.

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: Q3) Compute for y(x) = cos'(4vT)+ 5x and x(t) = 4 at t=1

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Q: Let f(t) = 4 sin(at) measure the height of waves in Horsetooth Reservoir with respect to time in…

A: The height function of the waves with time is ft=4sinπt

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

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Q: التاريخ الموضوع Find The approximate value of f(x) at X=1-2 whereof is defined over The period 1.7]…

A: The given table is To find: f(1.2)

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 the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

Q: If the derivative of the closed function x2 + 2x – 3y + y² +m = 0 at the point (1, 1) is available,…

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Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: t² – 1, ift 2 Vt +2,

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Q: t – 2 Find the values x where f(x) : dt has a local min/max. 2+ cos(2t)

A: Please rate.   Use Lebinitz theorem to differentiate the function.

Q: Suppose that the functions f and g, with linear approximations L, and Lz at x = a as shown below.…

A: Limit problem

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

Q: Suppose that the p.d.f. of X is as given f(x)=4x-1 for 0≤x≤1 and 0 otherwise Find the pdf of…

A: The probability distribution function of Y is:…

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: b) Use it in oonjunction with Simpson's 1/3 nule to integrate the same function for ive egmenta…

A: Introduction: Simpson's rule is a method to approximate a definite integral. The interval must be…

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: Suppose f(x) = x² + sin æ and F is an antiderivative of f that satisfies F(T) = 0. Then F(x) =

A: Solution..

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

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Q: implicitly dx

A: Solved 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.