Evaluate the limit: lim 2-1 (5x5 - 7x) =

Q: Find the derivative of f(x) = (-x6 - 3x² - 6x) sin(x). Provide your answer below: f'(x)=[

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Q: Without using a calculator, for the following, find rectangular coordinates for the given point in…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: i) Find the general term (an) of the sequence ii) Calculate 2e¹,5e-2, 10e-3, 17e-4,26e-5, 37e-6, ...…

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Q: Use the graph of y = f(x) to answer the question regarding the function. 10 -5 10 5 3) Find f(3) =…

A: From the given graph, we have to find the left and right limits at the point x=3.

Q: dx Assume that x = x(t) and y = y(t). Let y = x² + 3 and dt Find dy dt dy dt when x = 5. (Simplify…

A: We have to find the derivative

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= X-2 9x-4…

A: topic- equation of tangent line to curve

Q: x- /= ² + √²-11 de dx dx x-1 x² + x + 1 3

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Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. Q Ay 25- 20- 15- 10- 5A…

A: given,

Q: The series verges Justification: (converges, diverges) by applying the test.

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Q: Partial fraction decomposition can now be used to write L{y}, such that all terms have linear…

A: We can find the value of A and B by using the partial fraction method.

Q: 1. Explain why there is no solution to sec() and csc(n). You can use graphs and diagrams if you want…

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Q: Suppose dn 1 dt 10n and n(1)-2. Answer the following. 8) Separate the differential equation, then…

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Q: A thin wire is bent into the shape of a semicircle x2 + y² = 4, x>0. If the linear density is 4,…

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Q: If the average value of the function f(x) on [0, 3] is equal to 3 1 3/² 0 what is Select one: 0 6 O…

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Q: Find the power series for f(x) = ln(1 − x) centered at x = 0 by using term-by-term integration or…

A: Given  fx=ln1-x

Q: Evaluate and show all necessary solutions. 1.S cosxsin²x V1+sinx √25-4x² 2. S 3. S 4. fxcosxsinxdx…

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Q: Consider vector field: F = e i-cos y j+ sin² z k. Obtain divergence and curl for F at points (0,,).

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Q: Solve for w, where w is a real number. √6w-3=√8w-15

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Q: ∞ Σ η=1 7η + 3η gn

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Q: following

A: Please refer to the image below

Q: 3. State the remainder when f(x) = 2x² −x³ +1 is divided by (x+1).

A: We can find the remainder as below.

Q: One type of strontium has a radioactive decay rate of 1.4% per day. If 30 pounds of this strontium…

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Q: Find the derivative. F'(x) if F(x) = (ex² -3) 2² F'(x)=

A: use the natural log both side for finding the F'(x).

Q: Find the arc length of the curve defined by R(t) = 12t î+5costj+(3-5sint)k from t=0 to t=2. O 26 21…

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Q: 1. The graph of the derivative of the function y = f(x) is sl I y-f'(x) Determine the intervals when…

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Q: slope

A: Please refer to the image below

Q: Match the vector-valued function with its graph. r(u, v) = ui + vj + uvk -2-1 2 2

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Q: Find a vector-valued function whose graph is the indicated surface. The plane z = 4y r(u, v) =

A: Solution ) the plane      z = 4y   Let's make substitution  x =u , y = v  Hence  z = 4v   r ( u, v)…

Q: Question I The volume of the solid generated by revolving the region bounded by x² = 4y and y² = 4x…

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Q: Notice that if you don't use Equation 3.4, then NO CREDITS. 1. f(x)=1-x-x², a=0 2. 3. f(x)=√x+8, a=1…

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Q: 4. fxcosxsinxdx by parts

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Q: a) cot()

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Q: Evaluate the integral. I sin sin (3x) cos(6x) dx = NOTE: Enter the exact answer. + C

A: We can answer the integration as below.

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: Find the component of u = 2i + j − 3k that orthogonal to v = 3i – j, then verify your result.

A: This question can be solved using the concept of component of vectors.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 12e 1 + ²x |…

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Q: Let f(x) = x³ + 6x² - 63x + 25. (a) Use the definition of a derivative or the derivative rules to…

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Q: Without using a calculator, for the following, determine the definite integral that represents the…

A: Here, the given curve is r=3-4cos θ. The graph of the curve is: To find the area of the shaded(red)…

Q: 1. dx *² +4x+5 Sz

A: The given integral is ∫dxx2+4x+5 We have to find the integral

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

A: Note: To find the vertical asymptotes of a rational function, set the denominator equal to zero and…

Q: The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation.…

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Q: Without using a calculator, convert the parametric equations of a curve into rectangular form. No…

A: Given that parametric equation and convert this equation into rectangular form and State the domain…

Q: Question 18 A curve has a slope of 2x and passes through (1,4). Find the area bounded by this curve…

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Q: There are 11 identical circles drawn on a sheet of paper. How many ways are there to do each of the…

A: This is a permutation and combinations problem

Q: 3. An amusement park charges $8 admission price (P) and averages 2000 tickets (T) sold per day. A…

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Q: Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1. (A) 3.68 square units; (B)…

A: The region is bounded by the curves y=ex, y=x2-1, x=-1 and x=1

Q: Is z=xcosϕ ?

A: To determine whether z=x cos φ.

Q: Evaluate the integral with the aid of an appropriate u-substitution. Simplify the answer, if…

A: In this question we have to solve the Integral.

Q: (a) Use midpoint rule and trapezoidal rule with n = 5 to approximate the following integra- tion…

A: Given :∫-23x2dx    ,n=5