Use concepts learned in this module to complete this problem set: particle motion, applications problems with derivatives, related rates, local linear approximation, L'Hospital's Rule. 1. Determine the limit, showing and explaining your work: In x √√√x²-1 lim x→1.

Q: dz 4-1² Siv Ans. T

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Q: 42) 5,²2 x dx X+I

A: To evaluate the given definite integral.

Q: Let r(t) = ( −2+²+2, −3e¹, − 3 sin(2t)). Find fr(t)dt (don't include the +C) fr(t)dt = ([ ])+C

A: Topic = Integration

Q: Suppose that a price p and demand x are related through the price-demand equation  x+400p=8,000…

A: Given that x+400p=8,000 where x is demand and p is price Elasticity of demand = Percentage change in…

Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

A: Given: the radius of a circle increases at a rate of 2m/s. We need to findthe rate at which the area…

Q: Find the derivative of f(x)= x^13+8^x f'(x)=? please answer ASAP and write neatly Thank you.

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Q: 8)In the following questions, determine the behavior of h(x)=7x3+6x−x3+10x.

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Q: A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t), whose…

A: The velocity of the graph is increasing when the graph goes upwards.

Q: The reproduction function for a whale is estimated to be f(p) = -0.0005p² +1.02p, where p…

A: Given,          The reproduction function for a whale is estimated to be                     f(p) =…

Q: Evaluate the definite integral. 7 1 √₁² 36 + (x + 5)² dx

A: Here, we have given a definite integral and be have to find its value so we will find it by using…

Q: Which of the following is the proper format for the x³ + 1 partial fraction decomposition of (x²+4)²…

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Q: Simplify the expressions. (Use only positive exponents in your answers.) (a) (9x4)(−5x−3) =…

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Q: 4. Find all local maximums and local minimums for f(x) = x³ - 2x² + x - 1.

A: We have given function fx=x3-2x2+x-1 Derivative of the function is given as f'x=ddxfx…

Q: Given: (2x³ — x − 1) ÷ (x − 1) = 2x² + 2x +1 - Therefore: (2x² + 2x + 1) ÷ (X − 1) = 2x³ O True O…

A: The statement is false .

Q: Solve the following exponential equation. Express the solution set in terms of natural logarithms or…

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Q: Sketch the plane curve. (t)-4-. (0,4) y V 10 15 V 10 15

A: Sketch the plane curve

Q: Solve the DE. xdygda x² + y² O 2arctan(-) =e- +C ( ² ) = 2e=²¹² + C O arctan -xe-r2 O arctan(-) =…

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Q: Given the vector-valued functions 3t u(t)= e ti+e³tj - 2tk v(t) = 5ti - 4t²j+3k find (u(t). v(t))…

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Q: 2 32 32 0-22 3 y=5x-x2 y = x 1 2 3 4 (4,4) G

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Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

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Q: Calculate the derivatives using implicit differentiation: and ST of (TU-V)² ln(W – UV) = 1 at (T, U,…

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Q: Evaluate the integral. √2 sin 3 3 sin 6x cos 6x dx √2 sin ³6x cos ³6x dx = 3

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Q: Let f (x)= -6e^x +e^-1. Find f' (x). f'(x)=? Please answer ASAP and write neatly Thank You.

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Q: A farmer walks down a circular ladder from the top of a silo. With x, y, z in feet and the origin at…

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Q: Consider the function f(x) = = function on this interval. 1 on the interval [4, 7]. Find the average…

A: To use the mean value of theorem for the given function

Q: #8 Sunday, October 23, 2022 8:55 PM Use shell method to write and evaluate definite integral that…

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Q: Step 4 Solving 4x + 2y - 24 = 0 and 2x + 4y = 20 = 0 simultaneously gives 73°F Mostly cloudy X= y =…

A: Here,         We have given linear equations in two variables now we have to find out the values of…

Q: Use the given information to find the indicated probability. A ∩ B = ∅, P(A) = 0.5, P(A ∪ B) = 0.7.…

A: Topic = Probability

Q: If then f'(x) - f() = * sinh}(7a)

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Q: Calculate y' if y = 4log(x³e*)

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Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

A: On solving this we will get

Q: Given f (x) O-3 O 0 0 1 x+2 =2+2,g(x) = *=², find (ƒ + g) (1)? =

A: See the answer below

Q: What is the distance between the point (5,1) and the line with slope 2 and y intercept -2? 13√7 7…

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Q: Consider f(x)=x^4-2x^2+3 Note:Note: Use round parentheses for your intervals (open interval…

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Q: Given the following multiple representations, label and explain key features in context Tile Pattern…

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Q: Evaluate the expression. log 6274 log 6274= (Simplify your answer. Type an integer or decimal…

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Q: Consider the function h(x) = (x+1)f(x). Give the formula for the derivative h'(x). 1

A: Given query is to find the derivative.

Q: Solve the exponential equation by expressing each side as a power of the same base and then equating…

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Q: Suppose the position of an object moving horizontally after t seconds is given by the following…

A: According to bartleby guidelines when student post multiple subpart question then expert must have…

Q: 3. Show all work and solutions without use of a calculator: Consider the curve defined by the…

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Q: 8 Evaluate; give your answer in reduced proper fraction or mixed number: 1- 9 + G|5

A: 189+535

Q: A (green) as the graphs of a function and its derivatives: is the graph of the function is the graph…

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Q: How did you get the rewrite from sin^2(x)/sqrt(1+cos(x))

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Q: Evaluate the expressions. (Simplify your answers completely. Use only positive exponents in your…

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Q: x³ dr (1 + x²

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Q: using DESMOS calculator, shade the area that is INSIDE of r = 3 + 3 cos (theta) and OUTSIDE of r =…

A: The objective is to  share the area that is INSIDE of r = 3 + 3 cos (theta) and OUTSIDE of r = 3.…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 6 cos(t)i…

A: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 6 cos(t)i…

Q: y' = x - 2y cot(2x)

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Q: The marginal cost of manufacturing a yards of a certain fabric is C'(x) = 3 – 0.01x +0.000006x² (in…

A: We need to find the increase in the cost if the production level is rasied from 3000 to 8500 yards.…

Q: 5 Given k (x) = 6x +x, answer the following: Part: 0 / 4 Part 1 of 4 (a) Find k(-x). *(-x) - y

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