Evaluate the function: 1 dx x²/3 () 1+a!/3

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: Express (3*) dx as the limit of a sum. 1

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Q: Find f' (x) for 8 sin(x) f(x) = -; 7x2 – 8 sin(x) s'(x) = |

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Q: Integrate the following function by using trapezoidal rule. 142*dx

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Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: Find the intervals where the function f(x) = 2cosx + 1/ sin2x, 0≤x≤ 2π is concave up.

A: Let's solve.

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: Use implicit differentiation to find dy/dx. 3ey+4x2- 32 -11

A: Given information:The given function is y = 3exy + 4x2 – 3y2 = 11.The aim is to find the derivative…

Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: Use the Power Rule to compute the derivative: %3D lx=7

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Q: df Use derivative rules to compute where f(x) = -2xe". dx x%3DIn 7

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Q: Find the derivative of fG Cos' (3x²) 2. %3D

A: Consider the given function:…

Q: Use implicit differentiation to prove that la"] = d nxn-1 dx

A: ddx(xn)=nxn-1

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Consider the function f(x) whose second derivative is f''(x)=5x+3sin(x) If f(0)=2 and f'(0)=3 what…

A: Given : f''x = 5x + 3sinx

Q: Find f'a) for f(x)= =Sinx 1- Cos X %3D

A: We have to find the derivative of the given function.

Q: use the Power Rule to compute the derivative.

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Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: Differentiate the function. f(x) = sin(7 In(x)) %3D f'(x) =

A: Given function :

Q: ∞ sin2x dx (x²+1)²

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: Integrate the function. 2+81 dx 4x2 V In Vx2 + 81 + x x2+81 4x + C In Vx2 • 81 + x] Vx2 + 81 + C 4x…

A: Given,            ∫x2 + 814x2 dx

Q: · f(x) = sin(In r²) %3D

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Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Find f'(x) where f(x) = x*in(#) + (sin(x))".

A: Given that, fx=xsinx+sinxx To find the derivative of this fx=xsinx+sinxx, take the logarithmic on…

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Find the linear approximation for f(x)=sin2x at x=5π6 and use it to approximate sin2(147∘). Round…

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Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: f(-7 sinx + 3cosx)dx 4

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Q: Use the Power Rule to compute the derivative.

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If f(0) = 2 and f'(0)…

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Q: Find the derivative of f (x) = VI- 4z. To enter va, type sqrt(a). f' (2) = 固助

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Evaluate using Theorem - f(x) dx f(x) dx + | f(x)dx = |1 – e*|dr

A: Here The Given function is  f(x)=1-exand we have to evaluate∫-221-exdx

Q: find f'(x), where f()=Dcosx sin x.

A: The given function is, f(x)=cosxsinx. Obtain the derivative of the given function using limit…

Q: 1 3 + e2 + dx 2 (3х)3 2х2

A: The integral is ∫13x3-32x2+e2+x2dx. Evaluate the integral using u-substitution as follows.…

Q: Hi, I need help with this step-by-step please.

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Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: Find f tan-1 x dx by using integration by parts

A: We have to find out

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x)=8x+8sin(x). If f(0)=4 and f'(0)=4, what…

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Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,