1) Given lim *²+9x x-9x+9 a) Evaluate the limit algebraically. Show all work in a clear and organized manner and be sure to use proper limit notation where needed.

Q: Find a unit vector that is orthogonal to both i + j and i + k.

A: this is the question of vector  here lets assume that  a = i+j = <1,1,0> b = i+k =…

Q: = [5, −3, 7] and @` = [−1, 6, 2] For p = a) Determine px q`. b) Show your work to confirm that pxis…

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Q: Self-work: Sketch the derivative of the following function 1.6 1.4 1.2 1.0 0.8 0 1 2 3 X 4 5 6 Poll…

A: solutions:-Q3. roots of derivative ddxf(x)=0slope = 0 (represent horizontal tangent)according to the…

Q: Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the…

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Q: What is the difference between a definite integral and an indefinite integral? A student says: "The…

A: Detailed explanation is given below

Q: Solve sin(x) + 6 cos(x) positive solutions X = = 2 for the first 2 Give your answers accurate to at…

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Q: Find the inverse transform of the given function of s. F (3)=28+16 2s

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Q: The zero-product principle states that if AB then 0,

A: Given:- The zero product rule principle states that if AB=0 then___________.

Q: Exercise 3 Limit Laws and the direct substitution rule Assume that lim f(x) = 4 and lim g(x) = 9.…

A: To find out value of limit.

Q: In Exercises 83–90, perform the indicated operation or operations. 83. (3x + 4y)? - (3x – 4y) 84.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: In Exercises 1-10, factor out the greatest common factor. 2. 16x - 24 1. 18r + 27 3. 3x + 6x 5. 9x*…

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

Q: Rewrite - 3 sin(x) + 1 cos(x) as A sin(x + 6). A = =

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Q: (4) Evaluate 1 z² + 4z - 5 J -dz.

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Q: Find the derivative. (5x6+8x3)4

A: The function is given by y = 5x6+8x34 To evaluate: The derivative of the function.

Q: Eliminate the arbitrary constants y secx + 3x-²y³ = C

A: Let's eliminate arbitrary constants.

Q: Find the indefinite integral. (Use C for the constant of integration.) 72 ee +1 72 e +1 -x + C dx X

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Q: 17. Identify the conic section that the following polar equations represents: r = O A. ellipse O B.…

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Q: Evaluate the line integral F. dr where F = (3 sin z. -3 cos y, zz) and C is the path given by r(t) =…

A: We need to evaluate the line integral

Q: Why isn't factoring x* – 81 as (x² + 9)(x² – 9) a complete factorization?

A: A complete Factorization of a polynomial is the method to factorise the expression by puting all…

Q: Need help with this question

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Q: 7.21

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Q: The intensity of light (in appropriate units) passing through water decreases exponentially with the…

A: Given I(x)=10e-0.3x

Q: 8. Where is f(x)= x-3 if x≤3 x² if x>3 discontinuous? O A. 3 O B. [The set of numbers 1, 2, 3, ...…

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Q: Let f(x, y) =. Use the Linear Approximation at an appropriate point (a, b) to estimate ƒ(5.05,…

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Q: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (12, 1) in the form f(a+h, b+k)…

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Q: Finding the partial derivative Wyvt function W = cos (u²v) 13

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Q: Let Use the chain rule to find f(x)=1=-* f(2)=(5x+7-2) ². d dx -f(x)|a=1

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

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Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

A: neither maximum nor minimum attains.

Q: Use the chain rule to find the derivative of f(x) = 10√/7x² + 3x7 Type your answer without…

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Q: Evaluate the derivatives. Do not simplify. 4 (a) Find the 4th derivative of f(x) = √√x – 1 sin(3x) 3…

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Q: 13. Graph the solution set of the system of inequalities: y 8x - 3 O O A. <++++++ -20 10 B. <++++++…

A: Topic- System of inequalities We are given ,y&lt;-x+8 y&gt;8x-3 in slope intercept form , y=mx+c…

Q: Estimate the x- and y- intercepts from the graph

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Q: (a) Represent the function: x4 - 12x³ + 42x² - 30x + 9 and its successive difference in factorial…

A: The given function is; x4-12x3+42x2-30x+9.

Q: Please identify and sketch the level curves and traces of the curve 4x - y² - 2z = 0.

A: Level curve of function 4x-y2-2z=0

Q: Write the sum as a product: sin (11.7x) sin(3.7x) =

A: Solving the problem by finding the value of the product.

Q: (2) Evaluate sin³ x. cos²xdx.

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Q: Evaluate the limit lim xπ sin(x) X-T if it exists. If the limit does not exist, enter DNE.

A: Given, limx→πsin(x)x-π

Q: Explain the error in Exercises 106-108. Then rewrite the right side of the equation to correct the…

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Q: Find an equation for the plane consisting of all points that are equidistant from the points (2, 0,…

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Q: The following family of DE's depends on the parameter a. Sketch the corresponding bifurcation…

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Q: Find the area of the region that is bounded above by the curve f(x) = (x + 2)² and the line g(x) =…

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Q: 19. Translate the following limit notation into a sentence: lim(√x - 2) = 0 O A. The limit of √x-2as…

A: Given that we need to translate the following limit notation into a sentence.

Q: Let h(x) -5/x = 5₂ arctan(t) dt. Use the Fundamental Theorem of Calculus to find h'(x). 2 h'(x) = ||

A: Fundamental theorem of calculus states that if f(x) is continuous over an interval [a, b], and the…

Q: In Exercises 135-136, list all numbers that must be excluded from the domain of each rational…

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Q: If a + 0, the degree of ax"y" is

A: Degree of a term is the highest power of variable if term has only one variable and degree of term…

Q: Explain how to obtain the asymptotes for y = tanh x from the curvilinear asymptotes for y = cosh x…

A: Given function is y=tanhx .It is required to find curvilinear asymptotes for y=coshx and y=sinhx

Q: y = In x3 sinx 2 Cx² + 4

A: The function is given by y = lnx3sinxx2+4 To evaluate: The expression of dydx.

Q: Let Use the chain rule to find f(x)|x=1 f(x) = √6x² + 9x + 4. d - f(x)|x=1· dx

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Q: 2 For the given function, find (a) the equation of the secant line through the points where x has…

A: We will find the required.