Problem 1. L(x) = In 1.05 Find the linear approximation of f(x)= In x at x = 1 and use it to estimate In (1.05).

Q: Find the solution of the given initial value problem: y(4) + 2y"+y = 3t + 4; y(0) = y′(0) = 0, y″(0)…

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Q: x 5. r(x, y) = ln (x + y)

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Q: Given P(x) 3x55x² - 4x³ – 8x² 64x + 48, and that 2i is a zero, write P in factored form (as a…

A: NOTE: Refresh your page if you can't see any equations. . the given root is  so another root must…

Q: if f(4)=2 and f'(4)=2/5, use the formula (f-1)'(x)=1/(f'(f-1(x))) to find (f-1)'(2)

A: If f is an invertible function and if f(a)=b, then f-1(b)=a.

Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

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Q: 5x+7x-2 x² + 2 Identify the horizontal asymptotes (if any). If the graph of the function has a…

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Q: It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars…

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Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: Choose the correct answer. Derivative d O 9x9 O 8x10 09x8 .9 -x is equal to dx (Hint: Look at the…

A: Given problem:- Find derivative of x9

Q: You want to buy a triangular lot measuring 1360 feet by 1880 feet by 2430 feet. The price of the…

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Q: Find a bound for the error in the approximation T20 to the given integral (but do not calculate…

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Q: Evaluate the integral: -2 y√2y-y²dy

A: A detailed solution is given below

Q: O A. Use the formula for the cosine of the difference of two angles to find the exact value of the…

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Q: xp (I + ²)² [ (1) 9x)x I

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Q: +∞ Σ n=1 (x + 1)" 3°/m² + 1

A: Given Power series,∑n=1+∞x+1n3nn2 + 1

Q: 4Q Find the dot product and cross product of following vectors i a= 2i+j a= b=I-j+k b= 11. 111. a=į…

A: To find the dot product and cross product of the given vectors. Note that:…

Q: Find the solution of the given initial value problem: y (4) + 2y"+y = 3t + 4; y(0) = y'(0) = 0,…

A: Given differential equation,y4 + 2y'' + y = 3t +4

Q: Solve the following initial-value problems starting from yo dy dt A. = est y = = : 7. At what time…

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Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

Q: Solve the right triangle with hypotenuse 28 and one of the acute ngles 42°.

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Q: Without using a calculator, enter the sine and cosine of 240° using the reference angle. Decimals…

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Q: 12) 3 Find the first derivative of f(x)= -2 3x

A: The objective of the question is determine the first derivative of the given function.

Q: a B Find: b = Note: Triangle may not be drawn to scale. Suppose a = 10 and A = 60 ° C= C B = b A

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Q: Questions Identify the two regions that do not have a positive slope. What are they and what do they…

A: Given the graph distance time graph of a function. To find whether the slope is positive or…

Q: It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars…

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Q: (b) Find the derivative of f (x) = (x² + 2) (8x − 5) by using the product rule. Let g (x) = x² + 2…

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Q: +∞ x sin(x2) : = - Σ n=0 (-1)" .4n+3 (2n + 1)! X

A: Let's find 7th degree maclaurin polynomial.

Q: Questions Identify the two regions that do not have a positive slope. What are they and what do they…

A: Given a distance time graph. To find the whether the slope of the graph is positive or negative. How…

Q: Derivative 0 −4x-5 (Hint: Look at the note of section 2.3 example (c) in 0-4x3 0-4x-3 0 -4.x³ 4 d…

A: We can answer the question as below.

Q: /2 (e) [™¹², sin(x) cos(x)dx

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Q: 8. (x2 – 1)y" + 2y – (x – 1)(x + 1)2 = 0

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Q: Use the product-to-sum formulas to rewrite the product as a sum or difference. cos 20 cos 40 Need…

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Q: - Evaluate: [(5x¹ - 2x³ + 3x − 4)dx

A: We can solve the integration as below.

Q: (a) Find the derivative of f (x) = (x² + 2) (4x − 3) by first expanding the polynomials. Enter the…

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Q: 9. Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If…

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Q: QUESTION 1 Find the absolute maximum and minimum values of the function in the given interval. Use…

A: This is a problem related to maxima and minima of the function. please follow the procedure given…

Q: function X-1 if X<1 f(x)= 0 if 1≤X24 X-2 if X34 20 a. Graph the given b. define values where, it is…

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Q: Find the solution of the differential equation. 9y’’+6y’+y=0 theme: repeated roots; order…

A: topic:- differential  equations solution

Q: Prove that if A is an invertible matrix and B is row equiva- to A, then B is also invertible. ation

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Q: Solve 8 sin (7x) = 7 for the four smallest positive solutions

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Q: Find power series for the following functions x 1- (2x)4

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Q: where do these (encircled in red) come from?

A: I am attaching image so that you understand each and every step. Please take exact value then we get…

Q: Medium. Answer any two questions. 1. Find all three critical points for the function: f(x, y) = x²y…

A: The given equation is;  f(x,y)=x2y-xy+3y2

Q: 1. The point (-2, 5) lies on the circle whose center is at (-1,-3). Write the standard form of the…

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Q: Professor Calderon wants to build a rectangular fence along a pond so his dogs can go for a swim; he…

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Q: problem for x as a function of t. Solve the initial-value dx (t² − 10t + 21) = 1, (t > 7, x(9) = 0)…

A: The given equation is;  (t2-10t+21)dx/dt =1 (t&gt;7, x(9)=0)

Q: You throw a ball (from ground level) of mass 1 kilogram upward with a velocity of v= 35 m/s on Mars,…

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Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

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Q: Verify the identity. sin 5x √√2 (sin x- cos x) Write the left side in terms of a sum or difference…

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