lim (2x²+x-1) 2-0 LIMIT VALUE: 2²-4 lim 2-0 2+8 LIMIT VALUE: LIMIT VALUE: 9-z lim 2-9 3-√√2

Q: Find the equation of the line tangent to the graph of f(x) = (In x)5 at x = 2 MECHI y=0 (Type your…

A: Use derivative for finding the equation of line .

Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: Use AXYZ, as needed, to complete the given parts. Part 1: Z 15 cm Part 2: Part 3: Part 4: Y 7 cm X h…

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Q: a. f(x) = on [-1,4] 1²+2 b. f(x) = I√4-1² on [−1,2] c. f(x) = 2 sec r - tan r on [0,1]

A: At the  extremum of a function f(x), the first derivative is zero.

Q: b. √ ( 3 √ √x + ²) a dx

A: The given integral,      ∫3x+1xdx

Q: Match each graph with its equation. 1 a. = |2| 1 -√7

A: To match graph of given equations. y=xy=x3y=xy=1x2y=x2y=xy=1xy=x3

Q: Find the present value of a $30, 000 annual income stream if it is invested immediately as it is…

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Q: 1. y = 3x? – 2x4 - 3x3 + − − 2x + 1; y(4) - 8

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Q: 37-38 Evaluate the integrals by completing the square and ap- plying appropriate formulas from…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: -3.x Solve y" +4y=e¹³*

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Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

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Q: Question 4 > Find the domain and range of the function graphed below. -5-4-3 1 2 3 4 5 52 Domain:…

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Q: D Question 5 Find the derivative of -2x f(x) = x f'(x) = -2x²e-2x (E) None of these f'(x) = e-2x…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ||ti + 1²3|| dt =

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Q: The population of elk in a national park is given by the function 1000 P(t) = 1+15e-3t where t is…

A: This question can be solved using the concept of differentiation and limits.

Q: Find the average value of the function F(x,y) = x³ex++ the region 05x≤2 and 0≤ y ≤ x². over

A: Given problem:- Find the average value of the function F(x, y) = x3 exy +(y/x)2 +(y/x)  the region 0…

Q: In (x² + y² ) = 2 arctan y' 9 X

A: We know that derivative of xn is nxn-1.     Here i attached the solution of this question.

Q: 4. Use cylindrical coordinates to evaluate [!] √²³² + y²dv₁ D where D is the region that lies inside…

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Q: owin - y" −4y' +4y=0 L".

A: 1)  y''-4y'+4y=0 Auxillary equation is m2-4m+4=0m2-2m-2m+4=0m(m-2)-2(m-2)=0(m-2)2=0 ⇒m=2,2

Q: Suppose f(1) = 2² - 4z - 9. Compute the following: A.) f(-3) + f(2)= B.) f(-3)-f(2)= =

A: We can answer both the question as below.

Q: and a is in quadrant III and cos(3) = Given sin(a) = following: Note: You are not allowed to use…

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Q: y = x² + 2, y = 2x + 5, x=0, x=6

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Q: [CLO-21 f(x) and g(x) are functions that are continuous on the interval -3 ≤x≤2 and satisfy 1…

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Q: Decide whether the integral is improper. 1,01 In(x5) dx

A: We are asked to find whether integral is proper or improper

Q: d Calculate [ri(t) r2(t)] and Calculate[ri(t) r₂(t)] and [ri(t) × r₂(t)] first by differentiating…

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Q: 2. y=(2 tan² 20-1/²

A: To find derivative of given function.

Q: Find the​ producers' surplus at a price level of p=​$70 for the​ price-supply equation below.…

A: Given problem:- Find the​ producers' surplus at a price level of p=​$70 for the​ price-supply…

Q: Write the conjugate of √a +3

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Q: d [rı(t)- r₂(t)] = [ dt d [ri(t) x r₂(t)] = dt

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Q: Find the average rate of change of f(x) = 5x²-9 on the interval [2, t]. Your answer will be an…

A: Use the formula for the average rate of change of a function.

Q: 11. Given the function below, what is its derivative? * f(x) = 2x - √x f'(x) = 2x C f'(x) = 2 - a 1…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Evaluate the iterated integral. 8 3 (x + y²) dx dy -1/1

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Q: Find f''(x). 5 f(x) = (x² + 5) *

A: The given function,  f(x)=x2+55

Q: Find the limit. lim (t i − 3 j + t² k) 1-5 lim (t i − 3 j + t² k) − i 1-5 i k = i+ i j+

A: We can find the exact answer as below

Q: 9- Give five examples about application of polar coordinates in real life

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Q: y=x√3-2x³

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Q: 4 1. y = cost-sin ¹ t 2. y = (2 tan² 20-1)/²

A: Given : 1) y= cos4t-sin4t2) y=2tan22θ-112   To Find : Derivative of the given functions.

Q: A cat darts around a room chasing a ball. The cat first travels along the vector (-1,2) and then…

A: Given ,  A cat darts around a room chasing a ball. the cat first travels along the vector < -1, 2…

Q: Determine whether the integral is improper L' (x-4)-¹dx (A) Not improper (B) Improper

A: We can solve this as follows:

Q: Find the area bounded by r = 6cos (30).

A: Given: r=6cos3θ

Q: Given the function f(z) = 82-3, find and simplify the following values: f(a)= f(a+h) = f(a+h)-f(a) h

A: Simplify the expression at different values.

Q: The area of a triangle with sides of lengths a and b 1 and contained angle is A = a b sin 0. If a=2…

A: Use the application of derivative to find the rate of change.

Q: Use the properties of natural logarithms to simplify the expression. In(e) П

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Q: -. y ln x − x ln y = 4, y'

A: Given query is the derivative of the expression.

Q: Write an equation of the form ya sin bx or y=a cos bx to describe the graph below. 0 3 2 1 1 4 -100…

A: Check the amplitude and period of the graph and write the equation.

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Determine whether the improper integral diverges or converges. S™× x²e-x dx converges diverges…

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Q: Use the method of Laplace transforms to solve (O) 0 (0) 0.

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Q: Evaluate the limit A. ƒ(x) = 5x + 2 at x = 3 x²-9 B. f(x) at x = 3 x-3

A: A. f(x)=5x+2B. f(x)=x2-9x-3