Consider the function f(x)=x²- 5x. Compute the derivative using the definition f(x+h)-f(x) h by following the following steps. f'(x) = lim h→0 Evaluate and simplify. f(x + h) = Compute and simplify; f(x+h)-f(x) =

Q: = { x + 15 X C(x) = if x < 100 if x ≥ 100

A: Topic:- function

Q: Express the polar coordinates 5, 11t 6 in Cartesian coordinates. What is the point in rectangular…

A: Given: Polar coordinates 5,-11π6

Q: 4.y=log10 (x4 + 3x² + 1) 5.y = log5 √x² +1 1-x² 6.y-log10 |2–5x3

A: Given 4. y=log10x4+3x2+1 5. y=log5x2+1 6. y=log101-x22-5x3         Derivative of the log functions…

Q: dx x (In x)5

A:

Q: + 22/12 =)₁ y x² + y² dx + (ye³ +2²4₁²) dy = 0 =)

A:

Q: Compute the partial sums S3, S4, and S5 for the series and then find its sum. Σ(n+1-142) (Use…

A: Topic - sequence and series

Q: 43) B Find tan 0. 5 8 4 A

A:

Q: Convert the polar equation to a rectangular equation. Then use a rectangular coordinate system to…

A:

Q: Find the exact value of the following expression. cos (0) ... Select the correct choice below and,…

A:

Q: Find the limit, if it exists. lim X-- 12-1 xº-1

A:

Q: On the Fahrenheit temperature scale, water freezes at 32º and boils at 212º. On the Celsius…

A: Degree and Fahrenheit

Q: The derivative of f(x)=sec x is Select one: a. sin x COS X O b. C. O d. sin ² x 2 COS .X sin x cos²x…

A:

Q: 10. y = In(xtan y)

A:

Q: 1.Use interval notation to determine f(x)

A: Concept: The graph of a function: The graph of a function is the set of all points (x,y) in the…

Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x −…

A:

Q: Solve the differential equation [x a. b. C. d. y tan-¹ (²2)] dx + x tan¯¹ (2/1) dy = 0 c²(x²+y²) 2x…

A:

Q: Evaluate the integral: J22 SVA-2 01- [] π [] +C dydz 4-2² e² +²

A: double integration using polar form

Q: 8 S 1 Inxdr a. 0 b. 1 C. -1 ||

A:

Q: 15 Lo - - dx 15 X (x + 1) ²/ O 0 O or| 800 88 O 1 O 176 5

A: The answer is 0.

Q: 5. Which of the following expresses √175 in simplest form ? a) 5√2 b) 5√7 c) 7√5 d) 9√5

A: Given that, the number is 175.

Q: fferent rotations are called ard position by an integer multiple of resul an angle in standard…

A:

Q: ve passes through the point (0, 9) and has the property that the slope of the curve at every point P…

A: Topic:- application of integration

Q: Find the indefinite integral and check your result by differentiation. (Use C for the const (x³ -…

A: The given integral is ∫x3-12x-4dx use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C use the…

Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: 1. Karen is a hobby farmer from near Toowoomba in Southern Queens- land. She sells the lettuce she…

A: Topic- Functions and application of derivatives

Q: 4x² - 4x + 6 1x²³ + x² - 6x 3 use partial fraction

A: The objective of the question is evaluate the indefinite integral help of partial fraction.

Q: g(x) = (9) Find the critical values for x² + 4x+4 X

A:

Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

Q: 3 2 -1 2 we rational function f(x) = 1 3 Q 20 2.5r2 +4 > identify the int

A: Topic:- calculus       Definition:- If the second derivative of a function is negative on some…

Q: The area of the région bounded by the curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

A:

Q: Find the exact area of the region bounded by 2y = 4√√x, y = 4, and 2y + 2x = 6

A: Here we have to find the area of the region.

Q: 1. A ball is thrown upward from the top of a 12 meter high building at a speed of 25 meter per…

A: Given quadratic equation is H(t) = -17t2 + 25t + 12

Q: dv/du = (u - v)² -2(u - v) - 2.

A:

Q: Find the area of the surface. The part of the plane 3x+2y+z=6 that lies inside the cylinder x² + y²…

A: Since, the equation of the cylinder is x2+y2=4 and  3x+2y+z=6⇒z=6-3x-2yParameterize the surface of…

Q: applicable lim 13) Find the limit using L'Hopital's Rule if x²-4 x-2 X-2

A:

Q: Find dy. dx Please, expert, I do not have much money. Solve as many questions as possible, please…

A: To find the derivative of the given functions.

Q: 1 a 3 2 1 a 1 To find the blue shaded area above, we would calculate: b Where: f(x)dx = area 1 2 3 4…

A:

Q: √= - 4x + 43 x² 11x + 18 dx = +C

A:

Q: Given f(x)=e²x, determine the value of f(¹¹) (11th derivative)

A: Given  f(x) = e2x. We have to determine the value of  f11.

Q: = Express the following equation in standard form: y · 2(x + 2)² − 6

A:

Q: 7/2012 - y x² + y² (²) di dx + (ye³ +2²) dy = 0

A:

Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: If what does the following integral equal? - 11 [¯¯1² [8f(x) + 2g(x) — h(x)]dæ = - 68 - 11 [= f(x)…

A:

Q: g(x) = 10) Find the extrema for in [-5,-0.5] x² + 4x+4 X

A:

Q: Use the data and story to answer the following questions The table below shows the number of…

A: The number of state-registered automatic weapons and the murder rate for several North western…

Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

A:

Q: G 3 X lo dx si

A:

Q: Solve the differential equation [cos (2y) - 3x²y²] dx + [cos (2y) - 2x sin (2y) — 2x³y] dy = 0 - a.…

A:

Q: <X< 6 Submit Question 5 4 3+ 2+ -3 -2 -1 1 2 For the above rational function f(x) = 1 3 Q 17 2x²…

A:

Q: Find each limit, if it exists. 4- 8x 4x³-5 lim II

A: