3) If f is continuous everywhere and | f(x) dx = 6, find sec" 2x · f(tan 2x) dx.

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

A:

Q: \S(cos x)dx = 0 %3D

A: Let us consider f is continuous even function. Let f=x2 So, fcosx=cosx2=cos2x…

Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: If f (x) = cos(3x), then f' (-) is equal to

A:

Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: Find the limit of sin Ø/Ø as approaches 0°. * 00 1 -1 ООО

A: Using formula.

Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

Q: Find f'(÷) for f(x) = 2 sin z cos x

A:

Q: what is the absolute extrema point(s) of f(x) = e1-cosx on [ -pi/2 , pi ], if there are any?

A:

Q: The cdf of a continuous RVX is given by 0, x < 0 sin(Ax) F(x) = + 6x, A 0<x < 2A ° 1, 2A Find the…

A: The CDF of continuous random variable X is given by, F(x)= 0…

Q: What is the limit of sin when x approaches 0? Select one: O a. 1 O b. 0 O c. Does not exist

A:

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Find the open intervals on which the function is increasing or decreasing           f(x) = sin x +…

A: Given,

Q: 9. Differentiate y = cos(x3/2 In x), do not simplify. x2-4 Using Calculus, show on which intervals…

A:

Q: Find the open intervals on which the function is increasing or decreasing.

A:

Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(T) = 2.

A:

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

A:

Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: on f(z) = e cos x+ ie-Y sin x is entire.

A:

Q: If ƒ is continuous everywhere and 1| f(x) dx = 6, find | sec? 2x · f(tan 2r) dr.

A:

Q: Find the limit of the trigonometric function.

A: The given expression is limx→0cosx-sinx-12x

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(T) = 2.

A: We have to find

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

A:

Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

A:

Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

A:

Q: Find the limits sin(3t) lim In(sin(3t)) i+ In(tan(4t))" j+tln(3t) A t→0 sin(4t)

A:

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

A:

Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

A:

Q: Suppose f(x, y) = / tan(x) + y and u = (-3,0). Then, Du f(-0.8, 8) =

A:

Q: The function f(x) sin x + cos x is an even function. True False

A:

Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

Q: Use the closed interval method to find the absolute maximum and absolute minimum of f(x)= 2 cos x+…

A:

Q: How many periods of the function y = sec x are there between = and 3T -

A: Given: So, from the figure, it can be observed that only one period of y=sec x is there between -π2…

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

A:

Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

A:

Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: a(cos2x) sin(x-) TC 1. f(x) = tanx 4. What values should a and b take for the function fx) to be…

A:

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

A:

Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€…

A:

Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.