5x dx 4. To evaluate the integral J which of the following formulas can be used? V9+x10 du In(u + vu? + a²) + C 1. Va2+u? u?du 2. S (3b²u2 -4abu + 8a2)Va + bu +C %3D Va+bu 15b3 udu 2 3. S (bu - 2a)va + bu + C Va+bu 3b2 What is the function u ? Answer: u = What is du ? Answer: du = %3D Find the value(s) of a and b (if appropriate), and use the formula to evaluate the integral. [Use the letter 'C' for an arbitrary constant.] 5x*dx Answer: f orX+6^

Q: Immediately following an injection, the concentration of a drug in the bloodstream is 200 milligrams...

A:

Q: 1. dx (9+ e2r)

A:

Q: For the given p-series, identify pand determine whether the series converges. k=1 = Therefore the se...

A: p-series Test : The p-series ∑k=1∞ 1kp converges if p>1 and diverges if p≤1.

Q: Elimination of Arbitrary Constant: bxy +b*x+1=0;b is constant

A:

Q: (1 + +)' y =

A: As per the instruction, we will be answering only first question.  y'=1+1x3'    =31+1x21+1x'    =31+...

Q: (D² +D-1)² y =0 ,when x = y = 0 , y' = y' = 1 , y" = -1

A:

Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. 3...

A: The given curve,  y=x+2x-23 at x=1

Q: Lesson 1.7 12. In each graph, a parent function has undergone a transformation of the form f(kx). De...

A:

Q: The number of people P(t) (in thousands) infected t months after an epidemic begins 5 - where 1<t<12...

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly aks th...

Q: 8. 1 (b) 2 11k + 1 The series converges. eTextbo diverges. may or may not converge; it cannot be det...

A: A)∑k=1∞ 111k = 111+1112+1113+1114+.........+∞is the GEOMETRIC series with r = 111 &lt; 1As per the p...

Q: If f(x)dx=cot x² +C , then f (x) is equal to A -2cscx? B -2xcsc?x? © In/cscx²| D O In/sinx²|

A: We have to choose correct option for value of f(x)

Q: Use the Intermediate Value Theorem to show that f(x) = x^2 − 3x + 1 has at least one real zero betwe...

A: Given:- Use the Intermediate Value Theorem to show that f(x) = x2 − 3x + 1 has at least one real zer...

Q: A certain radioactive material follows the law of exponential growth. If between noon and 2 pm the p...

A: Let the exponential law of growth: As given: t=13.28 hours hence at night around 1:28 a.m., the de...

Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st state...

A: The given statements: Statement 1:    The dependent variables in ∂p∂r=∂3p∂x3-∂2q∂x∂r  are p and q.St...

Q: Activity 1: Determine the number at which the function is discontinuous. Show why Definition 1 is no...

A:

Q: Find the volume of the solid generated by revolving about x=0 the region bounded by the given lines ...

A:

Q: a. 15. A committee of three is to be formed from a group of four Math teachers and five Science teac...

A: topic - permutations and combinations

Q: Consider the function f(x, y, z) = ln(z² + 1) + yx². a) Find the gradient vector Vf(x, y, z). b) Wha...

A: To find out the gradient vector.

Q: Express the following sum in closed form. 6 +4. n k=1 k Hint: Start by multiplying out 6+4. n Note: ...

A:

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper f...

A:

Q: 7 1. f(x) = 6 {/x? – 20 {x* + 4 find f (4) (x).

A:

Q: Solve (x² + 4) y' = 2xy %3D

A:

Q: 9. 1+x

A:

Q: In the indefinite integral J 3x²e* dx, the integrand is A 3r © 3x2 D x³+C B.

A: The given integral,    ∫3x2ex3dx

Q: 3. v? – 4v = -1.2975 – 2.1i

A:

Q: Consider the function T = xe3x+y? dy 5 and dt where x = Vt + 1, and when t O we have y -2. dT when t...

A:

Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

A:

Q: Jack buys calculators for $6.00 each, envelopes for $.50 each and pens for $1.50 each. He spends a t...

A: Jack buys calculators for $6.00 each, envelopes for $.50 each and pens for $1.50 each. He spends a t...

Q: (x² +2x+3)(5-x 10. g(x)= 3x+2

A:

Q: A graphing calculator is recommended. The curve y = 1 is called a witch of Maria Agnesi. 1 + x2 (a) ...

A:

Q: curves

A: Please refer to the image below

Q: 19. e* +e = e**y

A: Solution ) ex + ey = ex + y  Differentiate with respect to x d/dx ( ex + ey )  = d/dx ( ex + y ) [ f...

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: This is geometric Progression series for convergence check common ratio

Q: A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere attache...

A: Question 5 A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisph...

Q: I. Analyze and sketch the following curves. Indicate critical points and label your graph. 1. y = 1/...

A:

Q: Consider the following sequence: S 7" {an} = 1=1 An+1 to show that the given sequence {an} is strict...

A:

Q: 8. If the longest side of a right triangle is 5.5ft and the shortest side is 3.3ft, find third side ...

A: Here, the longest side of the right is the hypotenuse whose length is given h=5.5 ft.

Q: 7. Determine the measure of an edge of cube whose total surface area is 150in.

A: the total surface area of a cube=6a2

Q: Find and classify the critical points of the function f(x,y)=3y^2 −12x^2 +12xy^2 +16x^3

A: Given function: fx,y=3y2-12x2+12xy2+16x3 Formulas used: ddxxn=nxn-1ddxconstant=0 To classify the cri...

Q: The volume V =ar° of a spherical balloon changes with the radius. a. At what rate (ft /ft) does the ...

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your...

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the constan...

Q: Activity 1: Determine the number at which the function is discontinuous. Show why Definition 1 is no...

A: A function f(x) is continuous at x=a if and only if limx→a+ f(x) = limx→a- f(x) = f(a).

Q: Find the projection of ū = (2, -3, 1) onto v = = (-3, 0, 1) %3D 3 0, А. B. (3.0. -1) В.

A: u→ =2, -3, 1v→ =-3, 0, 1v→ =(-3)2+02 +12       =9+1|v→| =10    u→  · v→ =2, -3, 1·-3, 0, 1u→  · v→ =...

Q: 2. y = 3x - 8x3 + 6x2

A:

Q: The function f(x) = 5x + 2 is one-to-one. %3D Find an equation for f '(x), the inverse function. ......

A:

Q: cosh (x) dx sinh (x)dx cosh (x) - sinh (x) is equal to ? B.I A.0 The definite integral of that funct...

A:

Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: F. Planes and Lines O Find an equatin The plane each of whose paints idistant to The agu w eq point ...

A: Here ,              We have given two points which are               equidistant from each points of...

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0 ...

A: To find the first derivative of y using the given equation.