Use the shortcut rules to mentally calculate the derivative of the given function. f(x) = 8x4 f'(x) = =

Q: Given that log¸× = 2 3 log, Y = 5 3 determine the value of log 109 21 27 2 (주)

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Q: solve the non-homogenous equation y” – 2y’ = t + e^t

A: The given equation is a non-homogeneous second order differential equation. The general solution of…

Q: Solve the following Differential Equations x²- a) y(-1) = 1 dx y²+1 b) + 2y = 3; dx c) dy - 4y = 4y²…

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Q: Using all your knowledge acquired in this unit during the last lectures, calculate the derivative of…

A: The given function equation is

Q: solve the non-homogenous equation y” – 2y’ = t + e^t

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Q: Let lim f(x) = 4 and lim g(x) = 6. Use the limit rules to find the following limit. x+4 f(x) + g(x)…

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Q: Consider the integral functional I(u = [ £{√1 √1+ [u'(x)]² dx Solve the minimization problem…

A: Step 1: Set up the Euler-Lagrange equation. The Lagrangian function is: L(x,u,u′)=1+[u′(x)]2​ The…

Q: Find the coordinates of the local minimum of the function f(x) = x²+3x²+5x.

A: The objective of this question is to find the coordinates of the local minimum of the function f(x)…

Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor serie f(x) =…

A: By using the definition of Taylor series to find the first three nonzero termsof the Taylor series.

Q: The area between f(x) and x axis given S₁ = 7, S2 = 10, S3 = 6, S4 = 5, find # 3 -3 -2 S₁ σ $ 4 A 4…

A: First, recall the Integral of the Function over Adjacent Intervals: If f is a continuous function…

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Q: Use the quotient rule to find the derivative of the given function. 2 8t² -5t f(t)= 9t +2 f'(t) = ☐

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Q: Determine whether the sequence converges or diverges, if it converges, find the limit. √1+4n2/1+n2

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Q: Let 4*.\ f(x) = t sin t²dt Find on what interval is f(x) decreasing. Find the second derivative…

A: SolutionWe need to find the first and second derivatives of f(x) and analyze their signs to…

Q: the total cost for printing x books can be given by the equation c(x)=1000+12x+(1/2)x^(2/3). use…

A: The objective of the question is to find the break-even point for the printer using Newton's method.…

Q: (2) Given the following level curves for an unknown function f(x,y), 9 25 Estimate the following.…

A: (a) Estimate f(3,0): To estimate (3,0)f(3,0), we need to look at the level curve that passes through…

Q: Complete the given table. (Enter the logarithm function in the form log(b).) Exponential Form 45 =…

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Q: Find the coordinates of the local maximum of the function f(x) = −x³ + 2x² + 3x.

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Q: If 2300 square centimeters of material is available to make a box with a square base and an open…

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Q: Evaluate the integral using the Fundamental Theorem of Calculus, Part I. (Use symbolic notation and…

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Q: 12. For the function f(x) = ax³ + bx² – 5x + 9, determine the values of a and b so that f(−1) = 12…

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Q: dw Use the case 1 chain rule to determine the derivative where dt ม w(x, y, z) = xez and x(t) =…

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Q: can explain what this question is so i could use it as an example

A: Let's break down the question and provide explanations for each part: G(0): This expression…

Q: Please can you help me witht he diferential geometry question I'm finding quite difficult

A: Step 1: Step 2: Step 3: Step 4:

Q: Typed

A: Given data:total = 10chocolate_chip = 4almond = 3oatmeal = 2high_fiber = 1 A. This scenario…

Q: R 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9 ≤ x² + y² ≤ 25 by…

A: The objective of this question is to evaluate the double integral of the function (x² + y²) over a…

Q: Let y = sin(4x). If ▲x = 0.2 at x = 0, use linear approximation estimate Ay Ay≈ = Find the…

A: The given function is  and

Q: Find f(x)=x³-21x²+19x+7 £fic concave DIS ON 1475 the inflection points.

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Q: 1 5. Given: cot(x)= π and 0<x<, find the value of the following expression using sum 20 and…

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Q: You plan to take out a 30-year fixed rate mortgage for $250,000. Let P(r) be your monthly payment if…

A: D. If the interest rate on the mortgage is 7%, the monthly payment will be $1663.26. The equation…

Q: f" (x) 0, nn +4 f' (n) = −n f' (n + 4) = n +1 f(n) = n f(n+4)=n+7

A: The given condtions are

Q: x3 14. Find the point(s) of the tangent to the curve h(x) = = - 5x28x+3 with same slope 4 3 as 48x +…

A: Step 1:Step 2:Step 3: Step 4:  Thanks

Q: 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9≤ x²+ y² ≤25 by converting…

A: The objective of this question is to evaluate the double integral of the function (x² + y²) over the…

Q: show all steps please! thank you!

A: The slope of the tangent line at point (x,y) is given as

Q: Select which one of the following statements is true for the function f(x) = 5x²+2x+3. 1 The…

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Q: f(x)=9x- -2 I => 4. Question Details Done Find the derivative using derivative rules. Simplify your…

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Q: Determine if the sequence converges of diverges, if it converges, find the limit. an = √1+4n2 /…

A: To determine if the sequence converges or diverges, we need to find the limit as n approaches…

Q: (e) 2π -π/2 |sin | da

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Q: Differentiate the following function. y =In5x = dx

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Q: A car is moving along a straight road. At time t seconds, the position of the car (in feet) is s(t)…

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Q: Find the derivative of the following function. y= (3x²+7) (4x+1) 5x-9

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Q: Use a calculator to estimate the limit numerically. lim x-0 6x 1 Select the correct choice and, if…

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Q: Find the general solution for the differential equation = -5 dy dx x²-9

A: The given differential equation

Q: Consider the given limits (a is a constant, f(x) > 0). lim f (x) = 0 xa limp (x) = ∞ xa lim g(x) = 0…

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Q: A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:

A: cartesian equation is y=7−631x​Explanation:Step 1:given that r=6sinθ+31cosθ42​using cross…

Q: A sign chart for f" can be used to tell where f is [Select] [Select] positive or negative continuous…

A: The objective of the question is to understand what information can be derived from a sign chart for…

Q: Find the first four terms of the Taylor series for the function 2 tan(x) about x = П 4

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Q: Find the derivative of the function. g(x)= 3 X-8 (4x+17)(3x-7) g'(x) = ☐

A: To find the derivative of the following function.

Q: 8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z…

A: The objective of this question is to understand the concept of directional derivatives and gradient…