3. Which of the following illustrates the Fundamental Theorem of Calculus? A) value at lower limit minus value at upper limit B) value at upper limit minus value at lower limit C) value at lower limit plus value at upper limit D) value at upper limit plus value at lower limit 4. Suppose the points of intersection of two curves are (1,2) and (6,7), and the area under these curves is evaluated using the fa f(x)dx. Which of the following has the correct limits? A) B) ff(x) dx f(x) dx C) f(x) dx

Q: (10) Explain how to calculate dr at the point on the folium of Déscartes

A: we have to find derivative

Q: 5. Determine the point intersection between curve y= x(3-x)and the line y= x. Hence, find the area…

A: To find the intersection points of the given equations y = x(3-x)  and y = x

Q: Find the Area bounded by the curves y? = x and x = 2y – y².

A: Draw the graphs of the given curves and mark the intersection area.

Q: f Gx,y) x+ 3 XY %3D

A: We have to check

Q: Suppose a function y = f(x) is continuous on a closed interval [a, b] and differentiable on the open…

A:

Q: Given the graphs of f(x), f'tx)and frx) determine x-coordinates of the points O 8, c,'D, E O show…

A:

Q: 8.) Let fx)= 2x³+3x +4 Use the limif definition of the derivative to calculate the derivative of f:…

A:

Q: on |+ え Discuss the Continuily et function fix)= !

A:

Q: a) Write down the definition of the derivative in terms of limits. Using this definition find (x² –…

A:

Q: What is the are bounded by the curve y = 6 cos x and the x -axis from x pi/6 to x = pi/2?…

A: Given curve,                    y = 6 cosx bounded by the x -axis from x =π6 to x = π2 The area is…

Q: If a function is not analytic at z=Dz, then Z, is called a O a. (a) and (b) O b. (a) only Oc.…

A: to choose correct option

Q: use the Fundamental Theorem of line Integrals to evaluate F. dR, where F (*.y) = < y. - X and C is…

A:

Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

A:

Q: Use Theorem I to compute the shaded area in Exercise 8.

A: By using the application of integration Area  under the curve y=-x(x-3) is given byArea=∫03y dx…

Q: A) If g'(x)>0 for all x in the interval (4,7) then g(x) is for all x on the interval (4,7).| B) If…

A:

Q: 1) Consider the function f(x) = 2x³- 5x² +8 over the interval [1,5]. a) Approximate the area under…

A: Given: 1) f(x)=2x3-5x2+8 and the interval 1, 5. To find: a) The area under the curve over the…

Q: c). Find the area under the curve f(x) = 4x +2x over the interval (5,8)

A: Given,            fx=4x3+2x , the interval is 5,8To find : Find the area under the curve over the…

Q: a) If the y-coordinate of the derivative function is negative over an interval, then the function is…

A:

Q: A baseball is "popped" straight up by a batter. The height of the ball above the ground is given by…

A:

Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

A:

Q: Use the definition of the derivative f'C)=lim flxty-PG4. to compuke derivative of flx)= 3X-X

A:

Q: Assume that the functions ?,?,ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c,…

A: given: ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c, h′(c)=d, f(a)=e, g(e)=ℓ,…

Q: 63. Prove a famous result of Archimedes (generalizing Exercise 62): For r < s, the area of the…

A:

Q: A) Give f(x)-V-3 find f-*(x) ,x >0 B) : Find the area bounded by the curve y = f(x) =v2x +1 and the…

A: We have to find  A) f-1(x) for f(x) =√(x-3)  B) area bounded by the curve y = √(2x+1) and the lines…

Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

A:

Q: m. 20 1 1 2 3 4

A:

Q: If g(x) > (x) on the interval [a,b), then the area between the curves for as xs bis given by: O A.…

A: See step 2.