1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

Q: Evaluate sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

A:

Q: Question 15 Find the area bounded by the curve y = -x 16 A 8 square units B 16 square units C10…

A:

Q: St. -4 16-x² A 4 (В 2 (C) 0 (D) None (Ε 8 00 dx is equal to

A: This is based on the definite integral.

Q: S (2 + x)dx √4-2x-x²

A: We can solve the integration as below.

Q: Evaluate and Solve the function using the product rule or quotient rule. Show your complete…

A: Our Aim is to evaluate and solve the function given below using quotient rule.y=2x3-35x+2 -(i)

Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

A:

Q: Find integral fraction (numerator) y dy / (denominator) square root of (y+2) using the substitution…

A: Let's find given integration by using given substitution.

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

A:

Q: Which of the following equations correctly states the Product Rule of Differentiation? dy = = f(x)g…

A:

Q: < d dx x² 2 tan t²dt=2x tan.x² (A) True B) False

A: Formula :

Q: 6) INVERSELY LOGARITHMIC The following information is given about a logarithmic function of the form…

A:

Q: Inx Complete the following table to evaluate the limit lim X-400 √x Step Explain the step In x lim…

A:

Q: If $S² A 2x²+x-2 (x+1)(x²+1) (В NIG NI- S None -dx= B(2x) +C1 14.0+. dx, then the value of B is…

A: We can answer the question for the value B as below.

Q: 5. Answer the following questions. (a) Sketch a graph of f(x) = |2²-9 and find the points c such…

A:

Q: 10 If if ff 10 1 [ f(x) dx = 12, then [ f(x) dx = f(x) dx = 17 and (A) True B) False

A: Given : ∫010f(x)dx=17     and  ∫810f(x)dx=12

Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

A:

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: 5. In another state, license plates are formed using 6 symbols, any of which can be a number of a…

A: We know, There are 26 letters A, B, C, . . . , Z and 10 numbers 0, 1 , 2 , . . ., 9.Therefore we…

Q: The most convenient way to evaluate A True B False S 2x-3 x²-3x+5 -dx is use Integration by Parts.

A:

Q: 8- (c) S e 1 x(lnx)³ 3 dx.

A: Compute the indefinite integral ∫e∞1xln x3dxApply substitutionu=ln x

Q: 3. S tan¯¹ √√x dx

A:

Q: QUESTION 14 I 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x==…

A: Find area between two curve

Q: S √(x-m+ 3. Consider 3x5 3x4+6x3-3x² - 6x A B C + + x-1 x+1 x+m -dx. Using the method of partial…

A:

Q: What will be the rate of change of the area of a circle with respect to its radius when the radius…

A:

Q: 8. fx(1+x)²/³ d dx 2/3

A: SOLUTION-

Q: -6 -4 -2 0 --2 (-2,-3) 2 6 4 (-1,-4) 1. Does this graph have a horizontal shift? If yes, state the…

A:

Q: 20. S dr √3-4r-r²

A: On solving this we will get

Q: If f(x) = =+10, then what is the value of f(a+h)-f(z) ? h - 1 (x+10—h)(x+10) 1 (x+10+h)(x+10). 1…

A: It is given that f(x)=1x+10. we need to find the value of f(x+h)-f(x)h.

Q: Given that dx 5₁² = missing steps = I due √x+2 √u Re-write the integral will all the missing steps.…

A: Given:     ∫-2-1dxx+2 Apply u-substitution:  Substitute u=x+2→dudx=1            dx=du Lower limit…

Q: Evaluate S= 3x5 3x4+6x33x2 - 6x + In O x-2 2 x² - 4x 2 O x² - 4x + In 2 x²-2x-In + In -dx using…

A: Given problem:-

Q: Determine the volume of the solid obtained by rotating the region bounded by y= x^2 and y=x about…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: y = 4 16 3x+3

A:

Q: Find the area bounded by the curve y=- 16 (A) 16 square units B) 10 square units 8 square units D 4…

A: If y=f(x) and y=g(x) are two continuous function on a,b and f(x)≥g(x) on a,b , then area bounded by…

Q: 9. 5 3 2 S 2 3 S ds

A:

Q: Let f(x) = 8x³ - 4. What is the value of c on the interval [0,2], such that f(c) equals the average…

A:

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2-4x about y=4 is to…

A:

Q: y = (2x − 1) (x + 4)

A: To evaluate and to solve the function using the product and quotient rule of differentiation.…

Q: Evaluate 3x5 3x4+6x3-3x2 - 6x S= -dx, using method of partial fractions.

A:

Q: S= Evaluate Ox² - 4x 2 Ox²–2x 2 O x² - 2x - In x² - 4x 2 3x5 3x4+6x + In 3x² - 6x - (x-1) 1/6(x+2)…

A: Explained below

Q: ·S- y dy y+2 A (√3+2-5) (5√3+2-y+24)+C ℗(√9+2-8)(5√3+2+7+21)+C Ⓒ(√3+2-5) (5√3+2+y+24)+C…

A:

Q: Find the area bounded by the curve 4 square units O 16 square units O 8 square units 10 square units…

A:

Q: (D² + 4)y = 4 cot 2x

A:

Q: Consider the triangle with vertices P(3, -4, 0), Q(4, -1, -2), and R(8, -3, -3). Determine the…

A:

Q: Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Given,  f(x)=ex

Q: 10. 3 J√cos z sin ³ zdz COS

A:

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2 = 4x about y=4 is…

A: Option C is correct  4-x^2/4

Q: Use the table to the right to find the given derivative. d xxx) 1x=5 (Simplify your answer.) |x=5 X…

A:

Q: X+2 √4x-x² 16. S dx

A: