Find the derivative of the composite natural exponential functions 1. f(x) = In x² x-2 2. g(x) = ln(√x³ + 1) 3. h(x) = ln(x² + 2x - 5)

Q: 1. f(3x + 1)¹5 dx 2. f(8x³ + 2x² - 1)7 (6x² + x) dx x-2 3. f dx √50-5x3

A: LetI=∫(3x+1)15dx put  u=3x+1differentiate du=3dxdu3=dxThereforeI=∫u15du3Take constant…

Q: Evaluate the following integrals: dx dx a. S b. f √81+16x² √16x²-9 C. S dx 49-4x²

A:

Q: 2. Evaluate x sin ædr using integration by parts.

A: Given: I=∫xsinxdx   We know the basic integration formula. ∫sinxdx=-cosx+C∫cosxdx=sinx+C

Q: Determine whether the function is a probability density function over the given interval. 35)…

A:

Q: 2. Find the Maclaurin series of f(x) = tanh ¹x

A:

Q: Sketch the region bounded by the given lines and curves. Then express the region's area as an…

A:

Q: Determine whether the series is convergent / divergent (4) Σ.Ξ1 +∞ 1

A:

Q: incorrect please re-provide

A:

Q: Let f(x)=x3−3x2−9x+25. Use the derivative f′(x)=3x2−6x−9 to determine the following values for f on…

A:

Q: Let g(x)= log4 (13-5x). State the domain of g using set or interval notation. . State the range of g…

A: g(x)=log413-5x Given function g is unbounded when 13-5x=0⇒x=135 The equation of the vertical…

Q: Evaluate the following integrals: dx dx ·S b. S √81+16x² √16x²-9 a. dx 49-4x² c. S.

A:

Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

A:

Q: A Prove that 1 B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x²+y²…

A:

Q: 10-x-x² if x 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

A:

Q: Determine the equation of the hyperbola with center (3, -3), a focus at (16, –3), and a co-vertex at…

A: To find out the equation of hyperbola.

Q: Show that the interval of convergence of the Series 2n-1 27-1 (4-3) IS given by -544/2 SWE

A:

Q: Let the vector v have an initial point at (−3, 4) and a terminal point at (-2, 6). Determine the…

A: NOTE: Refresh your page if you can't see any equations. .

Q: (A) (в Identify the form of the partial fraction decomposition of the rational function -3² +10…

A:

Q: Find the one-sided limits of f(x). Step 1 of 2: Find lim f(x). x--7 f(x) = -7x-3 -4x² + 4 if x < -7…

A:

Q: On the coordinate plane below, sketch the position vector (0, 3). PENCIL THIN BLACK

A: solution:-sketch the position vector 0, 3

Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 244

A: Using formula of area of circle

Q: In 23 In y SS 10 Evaluate the integral The value is. (Type an exact answer.) ₂x+y dx dy.

A: The given integral,     ∫0ln 23∫0ln yex+ydx dy

Q: 15. Si dt 1³ + 1² - 2t

A:

Q: Determine the number/s at which the function F(x)=√√4x² is continuous.

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the intervals where…

Q: In AGHI, h = 9.6 cm, g = 9.3 cm and /G=109°. Find all possible values of ZH, to the nearest 10th of…

A: We have to find the angle

Q: he sum of one number and four times the second is 24. Their product ust be as large as possible.…

A:

Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, cos x = 0, y() = 0…

A:

Q: y 3. The region bounded by the curve y=sec x, the x axis, the axis and the line x=0.25pi is revolved…

A: The given curves are; y=secx, y=0 x-axis, x=0 y-axis, x=0.25π So, the bounded region is as shown…

Q: Given the following matrix equation, which of the following is the correct matrix solution, A? -5 5…

A: We are supposed to find here matrix addition which we will find as.

Q: Evaluate the integral. π/4 Jo 0 sin5(x) dx

A: Given query is to find the value of the integral.

Q: Suppose F(5) = -4, F(6) = 4, and F'(x) = f(x). Sº f(x) f(x) dx = = Quest

A: Given problem:-

Q: Evaluate the integral. (Use C for the constant of integration.) [(sec²(t) i + t(t² + 1)² ₁ + t²…

A:

Q: S tanx 1+ COS X JX

A: Given problem:-  ∫tan(x)dx/(1+cos4(x))

Q: Sketch the region bounded by the given line and curve. Then express the region's area as an iterated…

A: Topic = Area

Q: 1 B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y²

A: To find all the second derivatives for fx, y=3xy2+2xy+x2 ln1x2+y2.

Q: Q5: Assuming that drag is proportional to the square of velocity, we can model the velocity of a…

A: We have to solve the problem using Euler's method.

Q: Consider the following graph. Step 1 of 2: Determine the intervals on which the function is concave…

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Differentiate and simplify this function k (t) = e√t^2+t+1 - e-√t^2+t+1

A:

Q: 2. The graph of f(x) is shown to the right and has the following characteristics. 100 f(x) = x55x4 +…

A: We can solve this as follows:

Q: 1. Given f(x)=x+5 and g(x)=x²+8x+15 Sketch the graph of y=- _f(x) g(x) Mark the asymptote(s),…

A:

Q: 8. 9. 10. Given f(x) = cos(3x + π), find ƒ'(π) a) 0 b) -1 c) -3 If f(x) = √ex, the derivative is: a)…

A:

Q: Let the closed interval [a, b] be the domain of function f. The domain of f(x - 3) is given by (A)…

A:

Q: Find the general antiderivative of f (x) = 4 x ln x²

A:

Q: Evaluate the integral In 23 In y s s ex+y dx dy.

A: Given: ∫1ln23∫0lnyex+ydxdy

Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

A:

Q: Find the centre and radius of the circle x² + y2² - 4x+6y-23 = 0. O centre (2,-3), radius 6 O centre…

A:

Q: Evaluate the spherical coordinate integral. 1- cos 2 2π π SS S p²sin & dp do de 00 0

A:

Q: =iven √x³√4-x² dx. If we letz= √√4-x², which of the following integrals is correct using…

A: We have to substitute z=√(4-x^2)