6. What can you conclude when dy is changing dx from positive to negative? A) fis at a local minimum B) fis at a local maximum C) fis not at a local minimum D) fis at absolute maximum

Q: (y®+ 4y³-Ay) dy y2+10 6. ,3.

A: LetI=∫y5+4y3-4yy2+10dyI=∫y5y2+10+4y3y2+10+-4yy2+10dyI=∫y5y2+10dy+∫4y3y2+10dy-∫4yy2+10dyTake constant…

Q: TRUE OR FALSE 10. Addition and Simplification can be applied to part of lines of proof. 11. If p, q,…

A: Here is the solution

Q: Convert to a polar coordinates. Show work. 13. (0,-4) |

A: polar coordinate

Q: 3.f(x) = (2x+3 if x =1 2 if x=1 4. (x)= {3+x if x s1

A: (3)f(x)=2x+3 if  x≠12     if  x=1limx→1-f(x)=limx→1-2x+3=5limx→1+f(x)=limx→1+2x+3=5f(1)=2it is…

Q: What is the slope of the tangent line to the curve a +y +¢y=3 at the point (1, 1)? O -1 O 1 cannot…

A:

Q: 6. S (10 x - 40) dx x 2 - 8 x + 15 8. S (e 5x - e 2x + 8) dx 2 e 5x 7. S 10 cot 2x dx

A:

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: Find the critical points of the function x -8x2 О 0,2, -2 O 0, 1 О 1,2, 3 this function does not…

A: Solution: Let f(x) = x4 - 8x2 find where f'(x) is equal to zero or undefined  f'(x) = 4x3 - 16x

Q: 8. The general solution of y" + 4y = 3 sin 2x

A:

Q: sec =zydy

A: Given

Q: 10. Simplify as much as possible: log (

A:

Q: 3. X sinx eas x dx 2.

A: To find out the integration.

Q: (MODULE 3& 4) ACTIVITY 1: Determine if the following functions are continuous at the given value of…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: 1 Evaluate dx. - 9x In(7e® + 1) 9x 1 -dx = In(|7+ e– 9æ|) + C 7+e-9x 7. 9

A:

Q: A circle has radius of 7 cm. What is the length of arc intercepted by a central angle of measure…

A:

Q: xp x[1+ (In x)²] 5.

A: The given integral is: I=∫dxx1+lnx2   ...(1)   We know that; ∫11+x2dx=tan-1x+C

Q: Suppose x? + y + z² = 1 and z = g(x, y) > 0. Determine g Su (글, 글). 1 1 2

A:

Q: x² – 2 (x + 2)(x + 1)² 1 + x + 2 x + 2 (x + 1)? x + 1 (x + 1)² Option 1 Option 2 1 1 2 1 x + 2 x +1…

A: The given expression is; x2-2x+2x+12   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: General solution of x dy = (2xe* – y + 6x2) dx

A:

Q: 2. Solve: 5 In(2x – 3) = 10 algebraically. First find the exact answer (no decimals or rounding,…

A: We have to find the exact answer and decimal approximation of given equation

Q: 4-2y -2 dx dzdy

A:

Q: 1) Find a power series representation for the function and determine the interval of…

A:

Q: Converting 49T radians to degrees will correspond to which value? (A -1746° -1674° -1764° -1476°

A: topic - radian to degree conversion

Q: 10) Find the linear approximation to g(y) = Cos(y+1) at y = 0. Use the linear approximation to…

A: Here, the given function is: g(y)=cos(y+1) To find the linear approximation of g(y) at y=y0=0 using…

Q: Given the vectors v and ü, answ v= 10i + 2j - 11k u=7i+24j a. Find the dot product of v and u. Find…

A: calculation of above requirement are as follows

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

A:

Q: Solution: Here * = Sin x The graph is Ine Shadded negion find i The required of we have to the area…

A: Let's find  area of given curves y=e^x from x=0 to x=1.

Q: Evaluate the following integral: 10x dx O 2

A: Integration

Q: 2. Solve the equation: y" – y " -2y' = 0 O y = cje* + c2 + cze2* O y = cje* + c2e* + c3e2*

A: The given equation is  y'''-y''-2y'=0

Q: Find S(-3e-3t + Vt)dt

A: Basic integration formulas are used. I have stated the used formulas in the solution.

Q: х3—х+1 Find: lim X→0 x2+3

A:

Q: 1. Find the area bounded by the curves y?=2ax, y?=4ax-a? 2. By integration, show that the area of a…

A: To find the area of the region bounded by given curves.

Q: Area under the curve y = 4 - x2  from x=-3 to x=3

A: Please see the answer bellow.

Q: Part B. Find the equation of the circle of curvature of the curve y = 2x* – x at its minimum point…

A:

Q: (Wh(2 - h)dh

A: To evaluate: ∫(h(2−h)dh Let I= ∫2h12−h32dh

Q: 2r³ – 4x² – x – 3 dx x² – 2x – 3 in |x + 1|+ 3 In|x – 3| + C in Ix + 1|- 3 Inlx – 3| + C Option 1…

A: Given

Q: Sketch the graph of f(x) = 2x + Vx*.

A: Given that we need to Sketch the grah of  y = 2x1/3 + x4/3  Now,  The graph is as follows

Q: Problem set 1 (Plane Figures) Solve the problems below using the following steps; i.) Sketch the…

A:

Q: Find the following integral 4sinxdx O -4 cos x + C O 4 cos x + C

A:

Q: Consider the following limt. lim - (x + 5) Find the Iimit L. (a) Find 8 > O such that |fx) - L| O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: False 1. If v, w, x E R" are vectors with v · w = 0 and w· x = 0, then v•x = 0 too. False 2. If v, w…

A:

Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral:

Q: Sove a lake, sere hft) represents the height above the water, in feet, at t seconds. a) Determine…

A: Topic:- application of derivatives

Q: The surface area of the solid of revolution of the region bounded by y = 2x, x = O and x = 2 about x…

A: Given: y=2x We know that surface area of solid of revolution about x-axis over the interval [a,b] is…

Q: 10. In writing a function in the denominator and its derivative is in the numerator, which of the…

A:

Q: Which of the following statements involving sigma notation is always true? η η η Α) E (ak bR) = E…

A:

Q: 7. Simplify tan n(cos" () ( cos-1

A:

Q: (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 (y – cos?x)dx + cos x dy = 0 + Ri = E, where L, R, and E…

A:

Q: 3. 2x°- 2x) dx x²+10 2 t1o

A:

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.