Homework Answers
![Substituting 2 ntr-/= =t (Qd+1 dardt when r=1 t=1 when 4= 5 t=85+5-1 t = = 29 29 I Į dt t 29 = [In(t) ] = ln (29)_ln (1) I =](http://img.homeworklib.com/questions/e180a640-3e11-11ec-bfdd-09e5d90aab3f.png?x-oss-process=image/resize,w_560)
. Find the first derivatives (dy/dx) for each of the following functions. Do not need to...
. Find the first derivatives (dy/dx) for each of the following functions. Do not need to simplify. (3 points each) A. y = (2x^5 + 3x^3)^2 B. y = (8x^3-56x^2+3x)/(x+12) C. y= (6x2 + 3x) (x – 4x3)
EXAMPLE 3 Find dx. 13 - 2x² SOLUTION Let u = 3 - 2x. Then du...
EXAMPLE 3 Find dx. 13 - 2x² SOLUTION Let u = 3 - 2x. Then du dx, so x dx du and 1 3 = 2x2 dx = = 1.I tu du 1 wrz du (27ū)+c 11 Il + C (in terms of x).
A) For the following scores, find the value of each expression: X 3 5 O 2...
A) For the following scores, find the value of each expression: X 3 5 O 2 1. Σx 2. Σx2 3. ΣΧ+1 4. Σ (Χ+1) B. For the following set of scores, find the value of each expression: X 3 2. 5 1 3 1. x2 2. (2x) 3. (X-1) 4. (x-1)2 C) For the following set of scores, find the value of each expression: X 6 -2 0 -3 -1 1. Ex 2. x2 3. (X+3) D) For the...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx....
Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx. -1 inner product (i) Prove that (p, q) defines on P3 an orthogonal (ii) Show that 1, х are (iii) Find the angle between 1 and 1 + x.
Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx. -1 inner product (i) Prove that (p, q) defines on P3 an orthogonal (ii) Show that 1, х are...
Question 5. Find the following indefinite integrals: 1. fre'de 4. .Js 3.f x In x dx...
Question 5. Find the following indefinite integrals: 1. fre'de 4. .Js 3.f x In x dx 6.[(x+5) Ževæ#5dx 2. f x sin 8x dx -5 (1 + In x) sin(x Inx) dx Sin2x sin x cos x dx 5. 7. 5 2x(x2 + 4)5dx 8. dx
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx...
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
L = sa V1 + [f'(x)]?dx = Se 1 + 2 dx dx Examples. Find the...
L = sa V1 + [f'(x)]?dx = Se 1 + 2 dx dx Examples. Find the length of the arc of the following curves. y = Vx3 fromx = 1 to x = 4 2. y = {(x2 + 2) from x = 0 to x = 3 3. y=*+ from x = 1 to x = 3 (Ans:*) 2x 4. y + from x = 2 to x = 4 8x2 5. y = -x2 - In x from...
MATH 241 S19 HOMEWORK 14 1. For each of theg, o dx (a) 4x3 + 7xy2 2Уз (b) x,5+1 xy + 1 2. For eac...
MATH 241 S19 HOMEWORK 14 1. For each of theg, o dx (a) 4x3 + 7xy2 2Уз (b) x,5+1 xy + 1 2. For each of the following, find y': (a). xy sin(xy)-b) cosxy2)-y2+x 3. Find an equation of the line that is tangent to the graph of x2y2 4xy 12y at the point (2,) 4. Show that the graph of xy1 and the graph of x2-y2-1 intersect at right angles. 5. Given that x2 -y2 -1, show that y"...
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7...
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7 2x+5) 5x2–2x+3 (ii) dx (x2+1)(x-1) x2+x+2 (iii) S3x3 –x2+3x+1 dx dx (x+1)V-x-2x In (x) dx (iv) S x2 X+1 (vi) S dx (1+x2) (vii) S dx x(x+Inx) (viii) Stancos x) dx (ix) 30 Sin3 e*(1 + e*)1/2 dx dx 2 sin x cos x (x) S B) Find the length of an arc of the curve y =*+ *from x = 1 to x...
EXAMPLE 3 Find dx. 13 - 2x² SOLUTION Let u = 3 - 2x. Then du dx, so x dx du and 1 3 = 2x2 dx = = 1.I tu du 1 wrz du (27ū)+c 11 Il + C (in terms of x).
A) For the following scores, find the value of each expression: X 3 5 O 2 1. Σx 2. Σx2 3. ΣΧ+1 4. Σ (Χ+1) B. For the following set of scores, find the value of each expression: X 3 2. 5 1 3 1. x2 2. (2x) 3. (X-1) 4. (x-1)2 C) For the following set of scores, find the value of each expression: X 6 -2 0 -3 -1 1. Ex 2. x2 3. (X+3) D) For the...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx. -1 inner product (i) Prove that (p, q) defines on P3 an orthogonal (ii) Show that 1, х are (iii) Find the angle between 1 and 1 + x.
Exercise 13. For each pair of polynomials p(x), q(x) E P define (p, q) р(«)q(2) dx. -1 inner product (i) Prove that (p, q) defines on P3 an orthogonal (ii) Show that 1, х are...
Question 5. Find the following indefinite integrals: 1. fre'de 4. .Js 3.f x In x dx 6.[(x+5) Ževæ#5dx 2. f x sin 8x dx -5 (1 + In x) sin(x Inx) dx Sin2x sin x cos x dx 5. 7. 5 2x(x2 + 4)5dx 8. dx
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
L = sa V1 + [f'(x)]?dx = Se 1 + 2 dx dx Examples. Find the length of the arc of the following curves. y = Vx3 fromx = 1 to x = 4 2. y = {(x2 + 2) from x = 0 to x = 3 3. y=*+ from x = 1 to x = 3 (Ans:*) 2x 4. y + from x = 2 to x = 4 8x2 5. y = -x2 - In x from...
MATH 241 S19 HOMEWORK 14 1. For each of theg, o dx (a) 4x3 + 7xy2 2Уз (b) x,5+1 xy + 1 2. For each of the following, find y': (a). xy sin(xy)-b) cosxy2)-y2+x 3. Find an equation of the line that is tangent to the graph of x2y2 4xy 12y at the point (2,) 4. Show that the graph of xy1 and the graph of x2-y2-1 intersect at right angles. 5. Given that x2 -y2 -1, show that y"...
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7 2x+5) 5x2–2x+3 (ii) dx (x2+1)(x-1) x2+x+2 (iii) S3x3 –x2+3x+1 dx dx (x+1)V-x-2x In (x) dx (iv) S x2 X+1 (vi) S dx (1+x2) (vii) S dx x(x+Inx) (viii) Stancos x) dx (ix) 30 Sin3 e*(1 + e*)1/2 dx dx 2 sin x cos x (x) S B) Find the length of an arc of the curve y =*+ *from x = 1 to x...
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