3. For the series 2 + 6 + 18 + 54 + etc., find; (i) the .... .. 12 term (ii) the sum of the first 19 terms.

Q: EXERCISES 1. What value(s) of c, if any, will satisfy the IVT for the given function f and the given...

A: topic - intermediate value theorem

Q: dy dr + y = x

A: We are asked to find the degree of the differential equation.

Q: Solve using the U-Technique Question 1 Consider the integral 2nx g(x) dx . There is a function g(x) ...

A: Given

Q: Consider dx and using u-substitution in rewriting the integrand as a function of u and du . x(1+vx) ...

A:

Q: 2:(y-x² )dx+ dy =0 1.

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 9. dx XV 81 - (In x)2 |

A: Here we will solve the given integral,

Q: If cotx 12 find the other trigonometric functions

A: We will use the basic trigonometric formulae to solve this question.

Q: (y² + x²y + 2x)dx + (x³ + xv+ 1)dy= 0; y(2) = -3 %3D

A: Given: y2+x2y+2xdx+x3+xy+1dy=0, y2=-3 We have to find the particular solution.

Q: 4. What is the domain and range of the parent function, and what is the domain and range of f (x)? H...

A:

Q: 3. Is the function given by Sx-4x-5, メ<5 X-5 2. continccus at x =52 Why ar whynot ?

A:

Q: Determine

A: We will find the critical points by equating the derivative to zero. 

Q: x² + y? = r2 O y = - y' = - y

A: topic - differential equation

Q: Write the first five terms of the sequence: 11 ln 7n) +00 In n n Determine whether the sequence conv...

A: Given: ∑n=1∞11ln nn

Q: 4. If x - xy + y = 1, find y 3x a.) x-3y2 c.) d.) ay b.) 1-3y2 3y2. 5. If 3x? +2xy + y? = 1, then y ...

A:

Q: Evaluate the integral. 5 x2 e dx +C

A:

Q: The average daily temperature at a tourist lodge is approximately T = 106 - 34 cos[ ( 4π ( t - 50 )...

A:

Q: Determine the a coefficient of the following quadratic equation and determine if this quadratic has ...

A: The given equation is -2(x-4)2+1  This is in the general form and i.e. a(x-h)2+k  By comparing, a=2 ...

Q: e3x Let dx be given . If u = e* + 1, then the resulting integral is S f(u) du. Compute f(3). ex+1

A:

Q: Show that f() find that root. (Use five iterations of the method by starting point xo = 1. You need ...

A: Given problem:- Show that f(x) = x3 - 2x - 4 has a root between 1 and 3 and use Newton's method to f...

Q: Consider the integral 2nx g(x) dx. There is a function g(x) such that when u = In x the resulting in...

A: Given query is to find the value of indicated function.

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A: Please see the below picture for detailed solution. 

Q: Question Let k(x) = (-3x² + 2x)g(x)h(x). Given the following table of values, find k' (-2). %3D -2 -...

A: k(x) = (-3x2 +2x )g(x)h(x) find k'(-2) =? k'(x) = (-6x +2)g(x)h(x) +(-3x2 +2x )(g'(x)h(x) + h'(x)g(x...

Q: Write the first five terms of the sequence: 11 ln n) +oo Determine whether the sequence converges, a...

A: To write the first five terms of the sequence.11 ln nnn=1+∞To determine whether the sequence converg...

Q: Consider the expression ſ V4 – x² dx = F(x)+C. The expression %3D F(2) – F(-2) is equal to

A: Here we have to evaluate F(2)-F(-2)=? We have, ∫4-x2dx=F(x)+C

Q: Prove that the given equation is a solution to the given DE: 1. %3D Gjезх + Сzе 2х + Сзе*; у" — бу" ...

A:

Q: Evaluate the following indefinite integrals. 1. Jx²dx 2. S(x³ + 2x)dx 3. S(a)dt :a = constant

A: Solving the problem by finding the indefinite integral.

Q: Evaluate f(3v+ dx

A: As per our guidelines we are only solve one question (i.e. the first question from start) and the re...

Q: cot 2x J Tcot22x – 15

A: Given problem:-

Q: Use the following graph and write the shaded area as integrals. A(-1,3) D(2,1) B(0,0) y= h(z) y = S(...

A:

Q: Plot the following functions y = (x – 1)3 + 2

A:

Q: Use the given definition to find f(A): If f(x) = a, + a,x a,x + ... + ax" is a polynomial function, ...

A: This is a problem related to matrix. We will find out square of the matrix and then calculate f(A) m...

Q: 1 (ke)3x For ſ k*e3*dx = + C. If u = 3x, then k =? 3 (1–In 2-1)

A:

Q: 58. Find the maximum volume of a cylinder inscribed in a core of 4 m volume.

A:

Q: Consider the integral 2nx g(x) dx. There is a function g(x) such that when u = In x the resulting in...

A:

Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13. Evalua...

A:

Q: The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m² and then divide ...

A:

Q: Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises 1-24. 2. а. rV x3 :...

A:

Q: 40. f(x) = -x' + 3x + 7, %3D

A:

Q: Find the particular antiderivative that satisfies the following conditions: 10 10 H' (x) Н(1) %— 0. ...

A: H'(x) = 10/x2 -  10/x7 find H(x) = ? so we have to integrate it H'(x) = 10x-2 - 10x-7 H(x) = -10/x +...

Q: equations

A:

Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value ...

A: we use the formula ddx(ax)=ax lna

Q: Find the indefinite integral. J. x cos 107Tx2 dx

A:

Q: 16. (sec x + tanx)² dx 32. sin? x cos x dx

A: We 1+ tan^2(x)=sec^2(x)  Also we integral of sec^2(x) is tan(x)

Q: Given: 2/(x)dx There is a function f (x) such that when u = -x, the resulting integral is 2du Evalua...

A: Need to find the function f(x). Given information: The integral is ∫2f(x)dxe-x3. There is a function...

Q: т?+2m Consider dm. If we let u = m + 1, what will be the resulting integral as a function of u? m+1

A:

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: As we know that the nth order Taylor's polynomials at x=x0 is given by; pn=fx0+x-x011!f'x0+x-x022!f'...

Q: If cotx 12 find the other trigonometric %3D functions

A:

Q: Write an equation for a sphere centered at the point (-1,2,3) with radius 8.

A: topic -  sphere 

Q: If we let u = 4x – 1 for theS 2 tan(4x-1)-3 cos² (4x-1) dx, what will be the resulting integrand? co...

A: Solving the problem by finding the integrand.

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: