Find the derivative of the function. In(e²x + 3) y =

Q: For a certain mammal, researchers have determined that the mesiodistal crown length of deciduous…

A: Given: Crown length (in mm) of the molar t weeks after conception L(t)=-.015t2+1.38t-7.1 To find:…

Q: dy Find by implicit differentiation. dx x²14xy + y² = 14

A:

Q: Solve the differential equation y` = (196+ y)²

A: The given differential equation is: y'=196+y2

Q: 1. Simplify the expression, that is, rewrite the following expressions as algebraic expressions of…

A: (a)  J=sec(arctan(x3))lrt tan-1(x3)=ytan(y)=x3we know 1+tan2x=sec2x

Q: d Q10 Compute [3t²] (a) 3t² (b) 6t (c) 0 (d) 9t

A: We need to perform differentiation.

Q: A stone is thrown straight up from the roof of a 256-ft building. The distance (in feet) of the…

A:

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A:

Q: A 200-foot cable weighing 5 pounds per foot is hanging from a winch 200 feet above ground level.…

A:

Q: (b) x dx dt 1 sin³ (15)

A: Given  x = 1sin8( t5 )

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A:

Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy = 0 dx

A:

Q: Let C(x) represent the cost of producing x units of a particular commodity where C(10)=1000 and…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given curves: y=x4, y=1 To find: Volume of solid obtained by rotating the region bounded by the…

Q: Find the points on the cone ² = x² + y² that are closest to the point (5,2,0)

A:

Q: 3. Find the centroid (, y) of the region bounded by y = 2 cos(3x) and y = 2 sin(3x) from z = 0 to z…

A: Centroid is given by x¯=1A∫abxf1(x)-f2(x)dx and y¯=1A∫ab12f1(x)2-f2(x)2dx where A=∫abf1(x)-f2(x)dx

Q: A student drew the graph of y = f (c), y = f' (x), y = g(r), and y = h(x). Unfortunately, they…

A: Find the graph of y=fx and y=f'x.

Q: The sum of integrals below give the area of a region in the xy-plane. Sketch the region, label each…

A:

Q: Consider the following equations. y = x, y=x²

A:

Q: Find the limit. lim X→0 sin (8x) 7x

A:

Q: 43 x

A: given diagram of polar region

Q: At exactly two of the labeled points in the figure below, which shows a function f, the derivative…

A: Given graph:-

Q: The dosage for a certain type of chemotherapy drug depends on several parameters of the particular…

A:

Q: The Third Gate You arrive at the third gate and look for the inscription. Your computer translates…

A: Given: Limits include an arbitary real number, c.Find the limits limx→c+33(x-c)2 and limx→c-33(x-c)2

Q: P'(W): = P(w) = 6w² - 2w + 4 VW

A:

Q: 3x³+1 f) lim x →∞0 4x³-1

A:

Q: Let S = {1, 2, 3, 4, 5). Let f S S be the function defined by f = {(1, 1), (2, 1), (3, 3), (4, 3),…

A: Sol:- To count the number of functions g: S→ S that satisfy the given condition, we need to first…

Q: Consi ider the ellipse 4x² + 2xy + 5y² The derivative = d on this curve is

A: Given: 4x2+2xy+5y2=149

Q: Use the Method of Undetermined Coefficients to find a particular solution to the equation and the…

A: The given differential equation: y''+3y'+2y=4x2-3ex ; y0=9, y'0=5

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

A: To sketch the region bounded by the given lines. Then to express the region's  area as an iterated…

Q: Evaluate the integral. 6e6t ¹+12° +35 S- 12t dt

A:

Q: Determine the PDE of all surfaces cutting the family of cones given by x²+y²-a²z²=0

A: The family of cones given by the equation:   x^2 + y^2 - a^2*z^2 = 0

Q: Suppose that f is differentiable at 1 and f'(1) = 1 = f(1). Evaluate x¹ f(x²+x-5) - 16 x²4 lim x-2

A: Given f is differentiable at 1 f'(1)=1=f(1) We are required to find limx→2x4fx2+x-5-16x2-4

Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

A:

Q: The area under the curve of the function f, using the Riemann sum, will be exact if we let the n or…

A: Solved below

Q: Complete the parametric equations of the line through the point (2,-6,-2) and perpendicular to the…

A:

Q: let y = 5 log (x+1) find y'

A:

Q: y" + 3y + 2y = 4x² 3 e² y (0) = 9, y' (0) = 5

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary…

Q: Use a substitution to change the following integral into one that can be found in an integral table.…

A: Given Integration: ∫7dvv3+lnv2

Q: Let f(x)= = 4x² tan(x) sec(x) 1. f'(x)= 8x*sinx+4x^2*cosx 2. f'(1)= . Find the following:

A:

Q: Find the point on the graph of the function f(x)=(sqrt x) that is closest to the point (18,0) .…

A: The solution is shown below-

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the 7+x…

A:

Q: Evaluate the integral. 2 √√Z T ||||** SS (² cos ²0+z²)r de dr dz 000 2 √Z T S SS (² cos ²0 +2²)r de…

A:

Q: 4sqrt(2) was incorrect

A: Given:= f(x,y) = x3y2U = (-3,3) P= (-1,-2)   The directional derivative being negative means that…

Q: Electric charge is distributed over the rectangle 0 ≤ x ≤ 2, 1 ≤ y ≤ 4 so that the charge density at…

A:

Q: Question 19 ( ) Let f(r) Inz for all z>0. Determine all intervals on which is decreasing.

A:

Q: Average Cost for Producing MP3s The average cost (in dollars) incurred by a media company each week…

A: Here is the solution:

Q: (a) Find the linear approximation L(x) of 2 f(x) = x³ at x = 3 L(x) = x = 27. (b) Use L(x) to…

A: The given function fx=x23. To find the linear approximation of fx at x=27.

Q: 1. Find the limit limä→∞ (1 + 3 X 5x

A:

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

A:

Q: z is incorrect

A: We have to find the value of z (Round to 4 decimal)