Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

Q: V. Directions: Find the extreme values of the given functions within the indicate 42-44. ƒ (x) = x²…

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Q: - 4. Find the area bounded by y = x - x² and y = x(x − 2)(x+2).

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Q: 4. The boundary of a field is a right triangle with a straight stream along its hypotenuse and with…

A: answer is in next step.  please give a like !!!!

Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics…

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Q: find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to the plane…

A: We have to find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to…

Q: The total cost of producing 1 unit of a product is given by C(x, y) = 80+ 0.3x² + 50y - xy dollars…

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Q: Evaluate the following limit, if possible. If the limit c 4 lim 42-√√

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Q: Find the formula for the sequence below: -5,15,-45,180,...   a an=-3(-5)n-1 b an=5(3)n-1 c…

A: We have to find the formula

Q: consider the function y=−3sin(4x−π/2)+1  a) What is the amplitude? b) What is the period?  c)…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: Find the derivative of each of the following functions. -6 8. f(x) = x +4x¹ 9. f(x) = 4x² +5x²³ 10.…

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Q: 5.The sum of two positive numbers is 16. What is the smallest possible value of the sum of their…

A: Let's find two numbers & smallest possible value of sum of their squares.

Q: Simplify the expression (1 - i)(√3+i) (1 + i)(√3-i) and express your answer in polar form where r> 0…

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Q: 4. Let sinx = Ź (-1)" x²n+) 2n+1 n=d ♦ a) Find a paver series for xsinx, Differentiate the power…

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Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

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Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

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Q: Solve the non-homogeneous linear recurrence relation. (note: the non-homogeneous part is a constant…

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Q: The amount of a certain substance in a chemical compound is given by the function C (t) = 20.6…

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Q: An 84 cm wire is cut into three pieces. The second piece is 4 cm longer than the first piece and the…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

Q: Perform the integration. 3 (13 (|3* − 1| + |3* − 3|) dx 0

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Q: 4. If a 32 foot chain is hanging (balanced) on a metal peg on a wall. At time t=0, with the chain…

A: Given that,

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Given: Now,     v(t)=f'(t)      =-16t2+286t+10'       =-32t+286

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y = 2x…

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Q: (a) Find the dimensions of a box with a square base with volume 125 and the minimal surface area.…

A: According to our guidelines, In case of multiple questions, we are supposed to answer the first…

Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: lim x4 1 x³-64 Ꮳ 5 1 vx2+9

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Q: A population grows according to the model, 1400 e 0.06t where A is the population t years after the…

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Q: Find symmetric equations for the line through the point (1, -2, -4) which is orthogonal to the plane…

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Q: Evaluate fx² cosh x dx

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Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

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A: We will solve the problem

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A: Using sine rule, length of other two side are evaluated.

Q: C. Find the slope and the equation of the tangent line to the curve. 23. y 2x−x+2 at (-1,5) 24.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 22. =2x²-3x+1 at (-1, 6)

A: Topic = Derivative As per guidelines , At a time only one question can be answered. please repost…

Q: The population of a city is 145,000. It declines continuously by 3% per year. ..... Assuming this…

A: Solution-

Q: A real estate firm estimates that the value of a certain property will be given by the function V…

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Q: 3. Find f'(a) if f(x)= e7x 2x + sin³ x

A: In this question, we want to differentiate the given function f(x) with respect to x.

Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function.

Q: True

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Q: p= I.F. = e/P(x) dx Now solve (I.F.) y = f (I.F.) - Q(x) dx 9. Solve the linear ODE using an…

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Q: 5. A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

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Q: Find dy/dx by implicit differentiation. (cos X + sin #Y)5 = 49

A: The given equation is;  (cos pi x +sin pi y) 5=49.

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: For the function f(x,y) = √y² + 5x², find f(2, - 5), f(− 1,2), f( – 3, – 5), and f(0,9). f(2,-5)=…

A: Given query is to find the value of the function at indicated points

Q: II. Find the value(s) of x (or the interval of convergence) for each of the following power series.…

A: The given power series,       ∑n=0∞n! xn

Q: tan x 4. f dx csc x sec (In x)dx 5. X dx 6. f 1- cos 2x

A: I have stated the used formulas in the solution

Q: (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a…

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