5. Answer the following questions. (a) Sketch a graph of f(x) = |2²-9 and find the points c such that f'(c) does not exist. (b) Determine the intervals along the z-axis on which the derivative in the following figure is negative. 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 -X 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Q: Sta tan" (x) sec4x dx _¹___tan (m + 1)(x) — —__¹___tan (™− 1)(x) + C m+ 1 m-1 ¹__tan (m + 2)(x) +…

A: To find the value of given indefinite integral.

Q: QUESTION 16 y dy Find of- using the substitution +5= √√y+2 √y+2 ² (√√y+2-5) (-5√/y+2+y+21) + C…

A:

Q: 5 dx Evaluate: (x-3)² 1 A B C D E -1 ∞o (does not exist) 1 0 None

A:

Q: Find y dy ·S- using the substitution +5= √√y+2 U /y+2 /y+2−5) (5√√y+2+y+24) + C…

A:

Q: Evaluate A B e Stam" (x) sec³x dx- -tan (m+3)(x) + m+3 1 m+2 -tan (m + 2)(x) + m −tan (m + 1)(x) — —…

A: Solved below.

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

A:

Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ( (1/4) Inx - B) + C? A 3 B 2 C) 1 D) 0

A: To solve the given integral problem.

Q: C) 8 square units

A:

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

A:

Q: [ sin(mx) cos(nx) dx. Suppose m and n are constants and mn. Evaluate 1 1 1 (A) -cos(m-n)x x+…

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: Question 14 The integral x dx can be transformed to which of the following using trigonometric…

A:

Q: Given: 3z = xy Find fy O xy/3 Oy/3 Ox/3 O None of the choices

A: We can find the partial derivative as below

Q: S²- 16-x2 A 2 B) 8 0 None 4 E dx is equal to

A: I am attaching image so that you understand each and every step. Option "C" is correct answer.

Q: y" + y = tanx

A:

Q: 4. t²dt /t° +1 3√/₁³

A:

Q: Evaluate the following. 1. [(sec 3x+cos3x)² dx

A:

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: Given the spherical tank with diameter 4m So the radius of the spherical tank R = 2m Weight density…

Q: 14. Solve the initial-value problem dy dt = -2y + u₂(t)e¯¹, y(0) = 3.

A:

Q: 14. sec xdx 2 3/2 (1 – 4 tan x)³/²

A:

Q: Question 11 Evaluate: S₁ 2 A 63 16 B 105 C) None 16″ D 105 E 2π - 63 sinxcos³xdx is equal to

A:

Q: If 10 f(x) dx = 17 and (A) True (B) False #free f(x) dx = 12, then 10 Sofo f(x) dx=5

A:

Q: dx 3-2x-x²

A: Evaluate the following

Q: Exercises To Solve [No.5] 6 "Cosx dx. Sin²x+25inx+5

A: Here is the solution

Q: Question 14 Find the area bounded by the curve y = - -x 16 A 10 square units B) 4 square units C 8…

A:

Q: Question Use the left-endpoint approximation to approximate the area under the curve of f(x) = +2 on…

A:

Q: Find S- y dy using the substitution u +5=√y+2. y+2 (A) (√3+2-5) (5√/F+2-1+24) +C 3 B…

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: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: 8. 5 cos²x - 3tan x COS X dx

A:

Q: 2x²+x+1 A (x - 1)(x + 1)(x-2) dx = ₁+ A -2 (B) None 3 D E 15 B x+1 + x-2 d. dx, then the value of C…

A: Given  ∫2x2+x+1x-1x+1x-2dx = ∫Ax-1+Bx+1+Cx-2 dx

Q: Write as a single function of a single angle. tan 145° tan 85° - = [?]([_]°) 1+tan 145°. tan 85°…

A:

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: Given

Q: Which of the following equations is 1011th derivative of h(x) = -5 cos x ? Oh(1011)(x) = -5 sin…

A:

Q: If tan A = and tan B B = 1/1, calculate and simplify the following: tan (A - B) = [?]

A: SOLUTION-

Q: (D³ - 2D + 4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

A:

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: We need to find area.

Q: π Find the area bounded by the trigonometric curves y = sinx and y=cosx" from X=- 3.459 square units…

A:

Q: If a particle moves on a straight line so that s = et (cost – sint) . Which expression can be used…

A:

Q: Find the area bounded by the curve 4 square units 10 square units 8 square units 16 square units 3 y…

A: Area

Q: π 5π Find the area bounded by the trigonometric curves y=sinx and y=cosx from x== to x== 4 4 (A)…

A: The region bounded by the curves y=sinx and y=cosx from x=π4 to x=5π4

Q: 15. cos³ 3x 3√√/sin 3x dx

A:

Q: Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x. Determine the area of region…

A:

Q: Evaluate A B с D S= 3x-5 3x4 + 6x3-3x2 - 6x x² - 4x 2 x² - 2x 2 x² - 4x 2 x2-2x-In (x-1) 1/6(x+2)…

A:

Q: The volume of the solid generated by revolving the region bounded by x²=4y and is to be solved using…

A:

Q: Moving to another question will save this response. 3x5 ·S. 3x4+6r3-3x2 - 6x 0 5 06 O 17/6 A Moving…

A:

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

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: If A B (C) E +x+ (x-1)(x+1)(x-2) 11 3 - <-2 11 3 None 3 dx = + B +dx, then the value of C is equal…

A:

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: To Find:Set up the integral for the work done in pumping the content to a point 3m from the top of…