Exercise 2. Find the following limits 3x +1 1) lim 2x +5 1-3x2 3x +1 2) lim X 2x +5 3) lim x- 2x+5

Q: 21. A rectangle is drawn in the first quadrant so that its base is on the x axis and its left side…

A: Derivative application

Q: 1 dv 5 3 v 2 –8v² +24v 2 –32v+16v 2

A: solution:-∫1v52-8v2-24v32-32v+16v12 dvlet v=t2dv=2t dt=∫2tt5-8t4-24t3-32t2+16t…

Q: After substitution is performed, which of the following is equivalent to xV4x² + 9 dx? 25 du 8. 25…

A: Here is the solution:

Q: Find the general solution of the given ODE x +1 y': y* +1 x? + r- - y? = x +4x + k Option 1 O Option…

A: integration

Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

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Q: 17. The base of a triangle is increasing at a rate of 2in/min. If the altitude is always twice the…

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Q: is this statement true or false   The probability of any possible value in a discrete in a…

A: Here is the solution.

Q: For the number 70260.011000 What is the number of significant digits and what are the significant…

A: Number of  Significant digits = 11

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Here, the given vectors are: P(0,0,0) & Q(4,5,4)

Q: Find the area of the specified region. 5) Inside the limacon r= 8 + 2 sin 0

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Q: y) dx +x dy = 0.

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Q: 1. Find r(9/2)=? 2. В (3, 2) %3D?

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Q: 4. Find the area between y=Z+3. and ys-xt1ox-9

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Q: 元 店sit sin? 4x cos² 2x dx

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Q: 10. By trigonometric substitution, we can transform dx into x*V4 - x2 A. Ssi'e sin ede В. 1 1 С. 32J…

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Q: 16. Given: [ S(x)dx=10; s(=)d& x = ? (x)dx= 3;

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Q: If f(x) = 4,/¤In(x), find f'(æ). %3D Find f'(2). Submit Question

A: Given

Q: The equation x² + y2 = 25 has O a center at (0, 0) and a radius with a length of five units. O a…

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Q: 7. SavT – 1 dr 8. | (x) Væ² – 1 dx 1 dx 5x +1 9. dx 10. 3x + 9 4x – 6 dx (x – 1) (x – 2) 11.

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Q: Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in…

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Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

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Q: 1/5 2n'5 3) Use the Limit Comparison Test to determine whether the series V5n + 7n+7 n=1 is…

A: Given problem:-

Q: Differentiate x + y = e2x+2y A. 1 – 2e2x+2y 1+ 2e2x+2y y' В. -1 + 2e²x+2y 1 – 2e2x+2y y' | С. ||

A: Given query is to find the derivative of the expression.

Q: An isotope of the element erbium has a half-life of approximately 13 hours. Initially there are 24…

A:

Q: 3. Write z = 12.2 - 31 in polar form. Use 3 decimal places.

A: The objective of the question is converting to polar form.

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: ind the average value of the function over the glven Interval and all values of x In the Interval…

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Q: Find the standard form for the TANGENT PLANE to the surface: : = f (x,y) = x cos (xy) at the point…

A: The given function is  z = f(x,y) =x cos(xy)

Q: Let g(8) = (2s – 1)°. Then g'(8) is 9'(1) is 9'"(8) is and g''(1) is

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Q: ady す。e o 25+x2 メp

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Q: Which of the following equations is a homogenous DE? O (xy? + x)dx + (x²y- y)dy=D0 O (x- y)dx+ (3x+…

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Q: P8: sin x cos x (2 sin x – 1)(sin x + 1)

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Q: Step 1 |an + 1 an + 1 n+ 1 1, or lim = 00, then n00 an Sa, diverges. For any fixed value of x such…

A:

Q: 4. A cherry pie with a temperature of 120°C was placed on a table to cool in a room of constant…

A:

Q: The demand for grass seed (in thousands of pounds) at price p dollars is given by the following…

A: The demand for grass seed in thousands of pounds at price p dollars is given by the following…

Q: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7

Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an: n-00 12) an…

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx. Write the given…

A: To find out the value of integral using the midpoint rule.

Q: Condense the expression to the logarithm of a single quantity. (log3(x - + 1) + 2 log3(x – 1)] + 6…

A: Let's find.

Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

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Q: 3. Sx³V4 + x² dx

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Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x2…

A: Let's find.

Q: Determine whether the series is convergent or divergent. If it is conve 00 2 (cos(26))k k = 1 Step 1…

A: Cos (26)= 0.647 Convergent Find the sum of series

Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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Q: Perform the following operations and express the results in rectangular form: a. (8.21+j4.31) –…

A: Rectangular form

Q: The differential equation (x²y-2x- 3)dx+ 2dy=0 O Linear in y Linear in x O Homogenous O Exact

A: Given a differential equation

Q: from e'dv Ve4v -16

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Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: Answer what is required in the problem. d 1 -dt 1+t dx .17

A: