Solve the following basic calculus problems: d а. cos x dx

Q: c). Find the area under the curve f(x) = 4x +2x over the interval (5,8)

A: Given,            fx=4x3+2x , the interval is 5,8To find : Find the area under the curve over the…

Q: Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in…

A: Consider

Q: Find the total area of the region enclosed by y=x^2 and y=2x by integrating with respect to y. A…

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Q: Given, f (x) = for æ + 3; f-1 (æ) x +2 x – 3 | Of-1 (x) x-1 3x+2 Of1 (x) = * Зх +2 x-1 x- 2 f-l (x)…

A: We have to find f^-1(x)

Q: dr 2.

A: Use simple integration formula.

Q: Determine an equation of the line tangent to the curve Y = 10 at the point with x- coordinate 1.…

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Q: dy I# 2x²y° - 3ry = at the point (1, 2)? 4x. what is %3D da O b) 2/3 O c) None of these O d) -43 e)…

A: Explanation of the answer is as follows

Q: 1. Rule 1: Add 2 starting from 9. Rule 2: Add 3 starting from 5. Sequence 1 Sequence 2 Ordered Pairs

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Q: Evaluate the sum: 2k), for n=21. k = 1

A: We can find the answer as below.

Q: Select the conic section represented by the equation. 3x 2 + 2x - 5y + 7 = 0 circle hyperbola line…

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Q: Let ü = and v =. If üxi = then determine the value of 3A+B+C. Answer: Finish attempt .

A: Find 3A+B+C=??

Q: Find the inverse laplace of s+3 s2-8s-9

A: Given,  s+3s2-8s-9

Q: Let f(x) = -0.4x² + 9x-12. Find the x-coordinate of the vertex. Round your answer to 2 decimal…

A: Giveen query is to find the x coordinate of the vertex.

Q: Find the unit tangent vector to the curve defined by 7(t) = (4 cos(t), 4 sin(t), 5 sin°(t)) %3D 37…

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Q: Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the…

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Q: Q3) A) If you have three functions: f(x) = x2 – x %3D g(x) = 3x – 1 %3D w(x) = x2 – 2 So, find gof…

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Q: Find the arc length of the polar curve described by: r = 5+ 5 cos 0

A: Use the formula for the arc length in polar coordinate.

Q: Let f(x) = (3x2 + 10x + 4)/(6 - 5x2). The horizontal asymptote is given by y = ? Round your answer…

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Q: (Drag and drop the missing words) ]sthe[ An of a definite integral as an endpoint of the interval of…

A: We have to fill in the blanks about improper integral.

Q: Question Given the function of f(x) = -7x2 -7 on the interval [0, 25], find arpoint c between 0 and…

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Q: x³y' – y? – x²y = 0

A: We have to integrate the above expression

Q: Answer the following True or False. If | (f(=) - 9())dx D. gives the area betvween u – f(r) and 1 -

A: Inverse function means it is the reflection along the line y=x. Reflection does not change the area…

Q: -x2 ca2+y? In cylindrical coordinates, , S S+V xy dzdydx = O a) None of these O b) So Só So 3 cos(0)…

A:

Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

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Q: A man borrows Php 100,000 from the Social Security System for a term of one year. The interest…

A: Bank Discount  =100000×15100=15000

Q: xsin x dx

A:

Q: Calculate the first, second, and third derivatives of = x' e2x (Use symbolic notation and fractions…

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Q: Approximate the integral using Taylor series method: xsin?x dx

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Q: Determine the value of 7A+6B if 19x2 + 41x + 16 A (x+ 1)² Cx +B (x – 1)(x +1)2 Answer:

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Q: If possible, find AB and state the order of the result. (If not possible, enter IMPOSSIBLE.) -1 6 3…

A: Given A=-16-3504 & B=3209 To find AB:

Q: Question The radius of a sphere was measured and found to be 2.0 cm with a possible error in…

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Q: 2. Rule 1: Subtract 4 starting from 20. Rule 2: Subtract 3 starting from 20. Sequence 1 Sequence 2…

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Q: Obtain the general solution for the following differential equation. (a) y" – (a + ß)y' + aßy = 0 (a…

A: To solve the higher order differential equation.

Q: 3) Determine if the series converges or diverges. If it converges, to 00 2* what does it converge?:…

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Q: Find out whether the series given below converges or diverges. 00 Σ 3n +4 n= 1 Choose the correct…

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Q: Find the area inside one leaf of the rose: r = 4 sin(30) The area is

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (3t + 4)i + tj, 0 <t<1

A:

Q: Find the area of the region bounded by: r 98 cos 20

A: Solving

Q: Find an equation of the tangent to the curve at the given point. x = 8 sin(t), y = t2 +t, (0, 0)…

A: The given curve,x=8 sin(t), y=t2+t at (0,0)

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: The graphs of ƒ(x) = x² + 5 and g(x) = -x² + 2 share two common tangent lines. Find the equations of…

A: Here we will find the equation of common tangent,

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx +5 at x-2? %3!

A:

Q: On the region x2 + y° 0, y > 0, the function f(x, y) = xy has O a) its absolute maximum of 6/3 and…

A: To find the absolute maximum  and absolute minimum of the function f(x,y) in the given region.

Q: VA? +3 +3dx

A:

Q: Current Attempt in Progress Consider the curve y = 6x3. The sketch of the portion of this curve…

A: Solve the following

Q: dy Q4) Find for the following functions dx 1. y = 2x + e2x-1 2. y = sec x tan x 3. y = t² + 2t t =…

A: Given

Q: Determine the conjugate radical of the expression -8+35. O-8 -35 O NE + 35

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Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

A: Since there are multiple question the first question is answered as per our guidelines. Kindly…

Q: 1) Evaluate the integral dy dx using polar coordinate

A: Explanation of the answer is as follows

Q: Let C1 be the curve with parametric equations x = cos t, y = sint – t, where t e [0, ). (a) Find the…

A: