2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

Q: 1a) The position of an object at time t is given by P(t) = 4t² − 4t + 3. Find the time t = a so that…

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Q: determine the open intervals on which the graph of the function is concave upward or concave…

A: Given query is to find the interval where function is concave up and down.

Q: List the points in the graph in the interval -1<x<7 at which the function is not differentiable.

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Q: Evaluate the definite integral. In 19 S 0 tanh x dx In 19 S tanh x dx = (Type an exact answer.) 0

A: F=∫0ln19tanhxdxwe know  elnx=xtanhx=ex-e-xex+e-x

Q: 3. Draw the graph of y = x² + 2 and the tangent line to this graph at x = −2.

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Q: 1. 2" Find the first five terms of the infinite sequence whose nth term is a₁= · 3" +1 work. Write…

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Q: For the function, find the point(s) on the graph at which the tangent line has slope 5. y = -0.025x²…

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Q: Let f(x)=√x - 4. a) Find f(x + h): b) Find f(x + h) – f(x): c) Find_f(x+h)-f(x). h d) Find f'(x): FI…

A: Givenf(x)=x-4   We are required to finda. f(x+h)b. f(x+h)-f(x)c. f(x+h)-f(x)hd. f'(x)

Q: 1 Use the properties of logarithms to write the expression as a sum, difference, or product of…

A: Given query is to expand the logarithmic expression.

Q: Example 5: (a) Show that the function f(x) = has a removable discontinuity at x = -2. x+2 (b) Define…

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Q: Differentiate the following function: f'(t) = FI f(t) = √t__1 1-1/1

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Q: Use the given graph of f(x) to sketch the graph of f'. y y y

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Q: Suppose f = 200x¹y and fy 200x¹y and fy = Make use of two antiderivatives f(x, y) = 160x5y³ +…

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Q: 2) Evaluate the following: a) [((sin² x) In(x² – 3x + 1)(tan¯¹ x)) dx] - dx

A: Given :ddx∫45sin2xlnx2-3x+1tan-1xdx

Q: Find the linear approximation to the equation f(x, y) = 4₁ approximate f(8.3, 2.13) xy 4 at the…

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Q: Which of the following is a consequence of the Intermediate Value Theorem without further…

A: Given f is a continuous function on -2,8 such that f-2=-1 and f8=7 , The Intermediate Value…

Q: 5. Let f(x) = 3x - x² x²-9 (a) Find all horizontal asymptotes of y = f(x) (or explain why there are…

A: The function has one horizontal asymptotes and two vertical asymptotes

Q: The point P(5, 37) lies on the curve y = x² + x + 7. If Q is the point (x, x² + x + 7), find the…

A: To find the slope of the secant line

Q: 11. Try again You have answered 1 out of 2 parts correctly. Let h(x) = f(x) · g(x), and k(x) =…

A: Given :- Let hx=fx·gx and kx=fx/gx

Q: Estimate the slope of the tangent line to the curve at the given point (x,y). The slope of the…

A: Topic = Function

Q: Evaluate the integral. π/6 π/6 Ï -π/6 -π/6 [(6 sin t)i + (6 + 5 cos t)j + ( sec² t) k] dt = 13.2.3…

A: A=∫-π6π6 (6sint)i+(6+5cost)j+(sec2t)kdtwe know  ∫sintdt=-cost+c∫costdt=sint+c∫sec2tdt=tant+c

Q: Find the absolute minimum and absolute maximum of on the closed triangular region with vertices…

A: This is question of calculus here function is given we have to find the maximum and minimum value of…

Q: Consider f(x) = x² + 6x + 7

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Q: Use logarithmic differentiation to find the derivative of y with respect to t. y=t√3t dy dt = C

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Q: Consider the function f(x) = -9x² + 54x + 1 on the interval [-4, 6]. Find the absolute extrema for…

A: The given function is: fx=-9x2+54x+1 &amp; x∈-4,6   Use the Power law: ddxxn=nxn-1

Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

A: To find the value of the derivative at x=2.

Q: 1 (x 1 + 4) - 0 (X-3) 2 호 + 1 (x

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Q: Solve the problem. The monthly cost of a certain texting plan is given by the function y-0.05x +…

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Q: 1. For the function f(x) = x² + 2, use the limit definition of derivative to find f'(-2).

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Q: Consider the following relation. ارما 3 -3 Step 1 of 2: Determine the domain and range for the…

A: Given:

Q: Find two natural numbers that are multiples of both 12 and 15.

A: To find the numbers that are multiples of both 12 and 15 For this we have find LCM of 12 and 15

Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x) = 24 - 6x²…

A: To find the volume of a solid obtained by rotating the region underneath the graph of  fx=24-6x2…

Q: Find all Where bothe the values of X the tangent horizontal 3 2 X²³ - 3x²³² - 8x +14 23 line 13

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Q: Use the table to find lim f(x) f(x) 13 13.9 13.99 14 14.01 14.1 15 10.8 10.99 10 11.02 11.1 lim_ƒ(¹)…

A: Note: For finding limits from the table we have to observe the limits how they are approaching in x…

Q: Find three positive real numbers whose sum is 75 and whose product is a maximum. Enter the three…

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Q: The solution set to |x-1|>|2x+1| is None of the above (-2,0) (-∞,0) (-2,00) (-∞, -2) U (0, ∞)

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Q: Find all solutions of each equation on the interval [0, 2T). 4 sin² x-4 sin x + 1 = 0

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Q: Consider the differential equation dy dx The differential equation has an equilibrium solution at y…

A: To find the limit of the give function.

Q: ²-8 If f(x) = X-4' X = where is f not differentiable?

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Q: Use the definition of continuity and the properties of limits to show that the function is…

A: here we use the definition of continuity.

Q: Find the derivative of the function using the definition of derivative. f(t) = 8t - 3t² f'(t) =…

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Q: Find All Solutions 3 sin z=3- 3 cos z

A: Given query is to find the solution of the expression.

Q: Graph the given piecewise function f(x) if x ≤0 if 0 2 f(x) = = {²- X- E 5 A (x - 2)² +1 3 42 B+ 5…

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Q: Using the definition of the derivative, find f(x). Then find f'(-2), f'(0), and f'(6) when the…

A: Here we have to find the derivative of function.

Q: ving integrais using x² +1 a) √x³+2x²+x x³ b) S x3+x²-x-1 x8 c) √(x+2)²(x-2)²

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Q: explain how you arrive the answer

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Q: Learning Target DC1: I can compute derivatives correctly for power and polynomial functions, and…

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Q: farmer has 1000 feet of fence and wishes to enclose a rectangular plot of land. The land borders a…

A: Given query is to find the length of the side for maximum area.

Q: The area under the curve y = 2.5-3.5 and above the z-axis between z = 3 and 2 = 10 is: area The area…

A: Given curve equation:- y=2.5x-3.5

Q: In a test drive of a new fuel efficient car, a company tracks the car's mpg (miles per gallon) for 2…

A: Given data, The table of approximation variation in the number of miles driven, Number of…