Find The derivatives: @-ª [secx - 5c0sx] d dx @y=3x²³ + sin x +5 cos x m yle) (sinx) y= и @y= 5 2 y= 2sinx X² 1t sin 2x x-tan 3x 1/1

Q: Find the local maximum and local minimum values of f using both the First and Secon f(x) = 2 + 6x² -…

A: Given that f(x) =2+6x^2 - 4x^3We have to find local maxima and minima

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Q: Consider a cylinder with radius 1, lying on its side, 3 units long. Now, we'll be using an integral…

A: Volume of the cylinder:-

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Q: Consider the function f(x) = 2sin(x²) on the interval 0 ≤ x ≤ 3. (a) Find the exact value in the…

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Q: The graph of f(x) is shown (see figure). 5x² f(x): = x2 (a) Find the following limit. L = lim f(x) =…

A: The given function is

Q: A 10-foot ladder leans against the side of a wall forming an angle with the ground. Given that the…

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Q: Water is pumped out of a holding tank at a rate of 5 - 5e-0.11t liters/minute, where t is in minutes…

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Q: (MC) A This is the only question in this section. Question If f (x) = cos x, then the Mean Value…

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Q: 2. A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

A: A rectangle ABCD is contained in the unit circle (circle centered at the origin with radius 1).…

Q: view Policies Current Attempt in Progress Find the area between y = x + 14 and y = 4x + 1 between x…

A: Giveny = x + 14, y = 4x + 1 and x = 0, x = 2

Q: Evaluate u³(²-1)² du in terms of u by expanding the integrand. [/u³(²-1)² du = -/( 11 + C 1) du

A: To evaluate  in terms of  by expanding the integrand.

Q: Using the figure below, estimate e 9 30 [²56x) 3 30 60 6 f(x) dx 12 15 f (x) dx. 15 Enter your…

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Q: Find the volume formed by rotating the region enclosed by: 3 6.9y and y = x with y ≥ 0 X = about the…

A: given function

Q: - 9 √²x²=2 dx = √² ((x² + 1) = 10) dx 1 + 10 1 +

A: ∫01x2−91+x2dx=∫01((x2+1)−101+x2)dx

Q: Apply the trigonometric substitution x = √3 sec(0). When determining the lower limit, you will have…

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Q: The BelgeGauffre company builds an ice cream cone from a round waffle of radius 10cm. They start by…

A: The given figure

Q: Area = 7 (a) What is [*5(x) 5 f²50 f(x) dx = (b) What is f(x) [ f(x)² is fºfo f (x) dx = [s (c) What…

A: Definite integral :- A deefinite integral has been evaluated between specific limits. This can be…

Q: 2. table. Speedometer readings for a motorcycle at 12-second intervals are given in the t (second) 0…

A: (a) To estimate the distance traveled by motorcycle during this time period using the velocities at…

Q: Consider the function f(x) = 14x - 4sin-¹. Find the critical number(s) off in the interval [-1,1].…

A: The given function is

Q: How many solutions does the equation sin 3x = 1.44−2x^2 ​have? Using Newton's method.  The equation…

A: sin3x=1.44-2x2

Q: I’m not really sure how to solve i’ve tried several times.

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Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = x² - 8x + 12 on the interval…

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Q: Consider the following line integral over the given plane curve. Use x as the parameter to write…

A: Consider the line integral

Q: A box is to be made out of a piece of cardboard 6 meters by 16 meters. Squares of equal size will be…

A: A box is to be made out of a piece of cardbord  meters by  meters. Squares of equal size will be cut…

Q: Write an integral in the form A region. Answers must be exact. As a suggestion, graph the equations…

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Q: Evaluate the following. [³√9+xªdx 9 + x4 dx

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Q: Find a general solution of the system x'(t) = Ax(t) for the given matrix A. -96 4-[-] A = - 15 9…

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Q: Find the value of k that makes the antidifferentation formula true [ (4x +1) 7 dx 4x + 1) ² dx = k (…

A: Integration helps to find the value of k.

Q: lim f(x) where f(x) = x→1+ X, x ≤1 1-x, x>1'

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Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 43 km/h…

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Q: A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a…

A: The objective of this question is to find out what percent of the original amount of water…

Q: If f(a) = 3 and f(x) is increasing on the interval [a, b], then which method of estimating the area…

A: If f(a) = 3 and f(x) is increasing on the interval [a, b], then which method of estimating the area…

Q: 0-5-5 x'(t) = -5 0-5 x(t). x( -5 -5 0

A: We have to solve the given initial value problem.

Q: Using the graph of h(x). identify all of the values of c for which h(c) is a local maximum of…

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Q: Consider the following. u =(4,-1,0) v = (-8, 9, 0) Find u x v. Determine if u x v is orthogonal to…

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Q: (a) Use the figure to find the [ f(x)dx. -3 value of VA f(x) dx? L²₁ f(x) dx = = -10 (b) If the area…

A: Question No. part (b):If the area of the shaded is , then to find .

Q: Find the x-coordinate of the point on curve y=In(2x²-11x) where the tangent line is horizontal. Just…

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Q: Which of the following vector fields are conservative? (i) F(x, y) = (7x6y6 + 5)i + (6x7y5 + 4) j…

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Q: Compute the line integral [(x+y)dx-xdy, where C is the arc of the parabola y = x² +1 that goes from…

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Q: A contractor drew up plans for an addition to a house. The new outside walls will be a total of 80…

A: A contractor drew up plans for an addition to a housse. The new outside walls will be a total of 80…

Q: Let y = 3e¹ 2x³+e-4z. . Which is y'? You will need to simplify to find the answer.

A: The given function is

Q: Find a formula for the polynomial p(x) that satisfies all of the following conditions: ● a degree of…

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Q: Given the values of the derivative f '(x) in the table and that f(0) = 195, estimate the values…

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Q: A particle starts from rest at the point (2,0) and moves along the x-axis with a constant positive O…

A: We have to find the graph of the distance of particle as a function of time.As we know that-As given…

Q: Let (a) 10.5 3.5 ・6.³.5 P f(x) dx = 9, [ r(x) dx = [ 3.5 10.5 a £10.5. f(x) dx = 4, and (b) (8f(x) -…

A: Given,

Q: 7. Find lim to talk A. 1 C. -1 B. 0 D. does not exist

A: We have to evaluate the limit.

Q: Suppose f is differentiable and f' is increasing on an interval (a, b) (that is, f is concave-up…

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Q: 1. Linear Approximations: The TANGENT LINE at a point can also be defined as a linear approximation…

A: The tangent line to a curve at a given point is a straight line that just touches the curve at that…

Q: When an object is removed from a furnace and placed in an environment with a constant temperature of…

A: The Newton's cooling law Temperature of the objectProportionality constant Enviornment temperature