Basic Catalus 1. f(x)- f(xth) = 5 (x +h) - Sx - 3 lim 5(x+h)-3- [5x-3] = lim 56 +5h -3 - 5% +½ h-70 = lin lim h-70 Onecking: d dx dx (5x) - (3) dx (3). dx D. 5 - 0

Q: 00 Determine el valor de a e R tal que: /" -dx e2x + 1 a ||

A: ∫1u2+a2du = 1atan-1ua+C

Q: a) Is the series >. is Vn + n3 + 10 n=1 convergent or divergent? justify your answers. 8.

A: We have to find the convergent test

Q: Evaluate the following definite integrals using the Fundamental Theorem of Calculus.  1. ∫13…

A: This question can be solved using the concept of fundamental theorem of calculus.

Q: Find the Indefinite Integral and 5x + dx (5x), Step 1 To obtain the glven Integral, rewrite the…

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Q: Consider the solid of revolution obtained by revolving the region between the curves y=0 and y=x^2…

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Q: Please

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Q: 3:) Consider the function g defined by g(x ,y) - cos ( TX VG) + loga (x-y) 3 (6) calculate the…

A: The function g(x,y) is defined byg(x,y) = cos(πxy) + 1log3(x-y)=cos(πxy) +…

Q: nd the sum of the following series. If it is divergent, type "Diverges" or "D". 3n 5"n! nswer. ote:…

A: To find the sum of the series.

Q: Find the rate of change of the surface area of the cube when the volume is 8 cm". A block of ice in…

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Q: (x- 2), (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A: This question is related to Straight lines, we will solve it using given information.

Q: 13-28 Sketch the region enclosed by the given curves and find its area. 13. y 12 x, y=x² – 6 14. y =…

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Q: x²+12x+12 dx x3-4x 1.

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Q: Compute the area of the region which lies to the right of the parabola x = y^2 – 12 and to the left…

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Q: (iii) y= x'e**, y = sin x+eec* (iv) sec x

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Q: Suppose we know that f(x)dx = 2 and g(x))dx. S g(x)dx = 7, find the exact value of S°F (x) %3D

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Q: If m s f(x) S M for a sxs b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Write the Taylor series for f(r) = a about z = 4 as en(x-4)". %3D Find the first five coefficients.…

A: The Taylor Series of f(x)= x3 with center a=4

Q: Let f (x) = 1(1 2 2 +4. Evaluate f(-8). f(-8) = Number

A: Given f(x) = -½(½)x + 4 We have to find f(-8)

Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: Given H=-29.53+1.073t2-0.2233t2 logt Here H  is head circumference Na t is the age function now,…

Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: separable 2

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Q: Find the arc length of y = +(x + 2)³ + (x + 2)-1 for 1 < x < 2. (Give your answer to three decimal…

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Q: 23. y = 2x, y=x, 0<x< 6

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Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

A: We have to sketch graph of parabola then identify the vertex, focus, directrix, endpoints of the…

Q: Find the sum of the series. 00 5n Σ 9"n! n = 0

A: we know  ex = 1+ x/1! + x2/2! +.....

Q: Find 9.) critical points b.) dope when x=1 c) Jaterral where the functim ) s increaing and…

A: As per our guidelines we are restricted to solve only 3 subparts of a problem. Please upload your…

Q: 8 dx I (x – 2)(x +6)

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Q: (-2)2n is En=1 00

A: ∑n=1∞-22nnn

Q: Consider the following integral. |Fe dt Find a substitution to rewrite the integrand as - Le" du. u…

A: To find the value of given integral.

Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

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Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: Let's find.

Q: Given the curve X = 2y – y and the line X = 0 Find the moment of R with respect to the y-axis M. y…

A: Given problem:- Given the curve x = 2y-y2 and the line x = 0 Find the moment of R with respect to…

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-2x. (Use…

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Q: . Find the derivative of f (x) = (2x – 6(3x²+8). A. 30x4-54x2+32x %3D

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Q: .

A: We will find the derivative.

Q: dx (x-2) Jx12

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Q: Question Given F(x) below, find F'(x). F(x) = V2r + 3 dt Provide your answer below: F(x) =N

A: We have to find the derivative

Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

Q: G'(0), where G(r) =| e * dt

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Q: J.) Frawate 822-27. 922-9 lim Deser mire the domain 6.) F(x) =「メー %3D

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Q: Find the arc length traced out by the endpoint of the vector-valued function 7(t) = t cos t î + t…

A: Solved below.

Q: dx I (x – 6)(x +2)²

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Problem #1: Differentiatef (x ) = [(4 x4 - 5 )(3 x2-9 x -5 ) ]3 and solve f (2). Solution: Reason:

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Q: Using integration, derive the La L(sinh at)

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Q: TUTORIAL 35 Given a function f(x) = 2x + 3x 1(x) is increasing and decreasing. - 12x - 5. Find the…

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Q: Kndly answer immediately   If f ‘(x) > 0 for all x = (a, b), then function f in the interval is a.…

A: topic- derivative of function

Q: Basic Coatalus 1. f(x) - f(xth) = 5(x +h) - 3 Sx - 3 lim 5(x+h)-3 [5x-31 56 +5h -3 - 5% +½ 1. lim…

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Q: solve 4cos^2(x)-13cos(x)-12=0 for all solutions 0<=x<2pie

A: We can find the solution as below.

Q: Find the product of the two matrices. Give me two answers at each number letter for the A.B and B.A

A: Since you have posted multiple question in this question which are not interlinked so i have solved…