Let f(x) = 6.1x² - 3.4x. Use the difference quotient and h = 0.001 to estimate the slope of the tangent line at x = 5.

Q: Consider the following function. =2323232 (a) Find the critical numbers of f. (Enter your answers as…

A: Given function:- fx=x2x2-9

Q: The surface area of a right-circular cone of radius r and height h is S = πr√² + h², and its volume…

A: Concept: Maxima and minima: The slope of a function can be found in its first derivative. The slope…

Q: Let f(x) = |x-10). Evaluate the following limits. f(x) - f(10) x - 10 0 0 lim z→10- f(x)-f(10) lim…

A: NOTE: Refresh your page if you can't see any equations. . here we have x=10

Q: в (х) = (x4+8xc)ex

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Q: d) Compute the angle in Degrees between ₂ and №3 Round your answer to 3 decimal places. Compute the…

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Q: 0 ven ₁ = 10 9 -8 (:). -8 compute the cross products as listed. -5

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Q: Find the indefinite integral. (Use C for the constant of integration.) [(8) (8 cos(x) + 7 sin(x)) dx

A: We can solve it by finding the indefinite integral in the below steps.

Q: Determine if the differential equation (2xy^2 + 3x^2)dx + (2yx^2 + 4y^3)dy = 0 is exact. If the…

A: As we know that: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. Then the…

Q: Find the derivative of the function. y = sin²(x² + 7) y' =

A: Given, y= sin2(x2+7) Formula: sin2x = (1-cos2x)/2

Q: Find the minimum and maximum values of the function subject to the given constraint f(x, y) = x² +…

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Q: Let f(x) = 4x + 19 √x+13 2 if x if x = T 4 4 4

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Q: d'y Find for the curve given parametrically dx² by x(t) = 4+t², y(t) = 1² +2+³.

A: Correct Option =first option

Q: A construction worker pulls a five-meter plank up the side of a building under construction by means…

A: Topic- Application of derivatives. We are given, Worker pulls the rope to which plank is tied at a…

Q: 7. Consider f(x)=√x a) Find the linear approximation for f(x) near a=36 b) Approximate √36.005 using…

A: For (a), The linear approximation of the function fx at point a is Lx = fa+f 'ax-afx=x,  a=36Lx=fa+f…

Q: The point P(16, 7) lies on the curve y = √x + 3. If Q is the point (x, √x + 3), find the slope of…

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Q: Find the derivative. (e-2x) (x4)

A: Derivative of given function =ddxx4e-2x

Q: Evaluate the following iterated integrals For you to Solve: 3: 22 So So So x y ² z ² dz dx dy 2 x-y…

A: We have to evaluate the given iterated integrals.

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos(x), [0, 2π] minimum…

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Q: Find the direction N from P0(sqrt(π)/3,sqrt(π)/2) in which the function f=sin(xy) increases most…

A: Given the function f(x, y)=sin(xy) Find gradient of function…

Q: Find the GS of y" - 2y' + y = 0

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Q: Find the exact length of the curve. y = In(cos(x)), 0≤x≤ I x≤ 6

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Q: Find the minimum and maximum values of the function f(x, y) = x² + y² subject to the given…

A: Recall: Method of Lagrange multipliers

Q: The total cost (in hundreds of dollars) to produce x units of perfume is C(x) = 3x-8 2x+9 (a) Find…

A: Given, C(x)=3x-82x+9

Q: Let f(x) = (3x+ln(x)) / x+3  Find f'(x)

A:

Q: Determine the x-value of all critical points for the following function. 2 X² X-7 f(x) =

A:

Q: 3) An oven is preheated and then remains at a constant temperature. A potato is placed in the oven…

A: Concept: Given the equation to represent (T) temperature at a given time t Putting the values of (T)…

Q: 2) Use guessing to find particular solutions to the following equations. d) y" - 2y' - 3y = 2e 10…

A: By guessing to find the particular solution of the following equation. y''-2y'-3y=2et-10 sin t

Q: We are going to calculate the derivative of the following function using the Chain Rule (or more…

A: Given query is to find the derivative of the function using chain rule.

Q: Let f(x, y) = 1 + x² – cos(5y). Find all critical points and classify them as local maxima, local…

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Q: Consider the polynomial g(x) = x³ + 5x² - 12x - 60 a. List all possible rational zeros of the…

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Q: Equations of Order One: Separation of Variables Instructions: Obtain the general solution of the…

A: To solve: y' = xy ⇒dydx = xy ⇒dyy = xdx

Q: Evaluate the radical expression and express the result in the form a + bi. 6 √-36 6 + -36

A: See the answer below

Q: 2. Let m and b be rea If fis both continuo

A: Topic:- calculus

Q: explain why the graph is discontinuous at x=1 1= { * 1 f(x) = X²-X IF X 1 if X = 1 X²-1 Sketch the…

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Q: 2. Let f(x) be a continuous function on the interval [0, 1], and suppose 0≤ f(x) ≤ 1 for all x = [0,…

A: in this question we prove the above two results.

Q: Evaluate the following integrals. a. Cπ/4 f/4 cos 20 de

A: Since you have posted multiple question in this question which are not interlinked so i have…

Q: 1. x²-2x-24y+1=0 Standard Form Equation: a. Vertex: b. Focus: C. Length of LR: d. Directrix:

A: Topic = Parabola As per guidelines , At a time only one question with three sub-parts can be…

Q: Find the derivative. (e-2x)(x4)

A: Topic = Derivative

Q: c+1 for all real numbers E cical points is negative and the ver is not an integer or with am pe no…

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Q: Differentiate the following functions and simplify. Hint: you might use the logarithmic properties…

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Q: 8 - (₁₂).- ().- (*). - (1). , = = , U4 = -9 5 -6 Given U₁ = , compute the operations listed.…

A: We will find the required dot products for the part a, b and c as following.

Q: Find two positive numbers that satisfy the given requirements. (Enter your answers as a…

A: Given query is to find indicated unknown numbers.

Q: Find when dy dx x(t) 1. 2. 3. 4. 5. 6. dy dx dy dx dy dx dy dx dy dx dy || = tlnt, y(t) 1+ ln t 2…

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Q: 3. h(x) = 4x² + 4x + 3;h(x) = 0

A: Explanation of the answer is as follows

Q: Find the critical points, domain endpoints, and local extreme values for the function. y=5x√16-x² 2

A: Given, y=5x16-x2

Q: 2) Use guessing to find particular solutions to the following equations. e) y" +6y' + 13y=e-²t cos…

A:

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a =…

A: Height is 7.111 unit.    And volume is 40.21 unit3.

Q: cos(m + √5) + tanh¯¹(sin² m) = In 3+ y sech ( 1² )

A:

Q: Given the quadratic function in blue and the line tangent to the curve at A in red, move point A and…

A: Detailed solution is given below

Q: a) lim f(x) X→-3+ (b) _lim_f(x) E 1 0 (c) lim f(x) x--3 (d) lim f(x) x→ 2-

A: