Determine the derivative of each function using the limit definition. 1. y= 2 - 7x 2. f(x)= 4 -5x - 2x2 3. y= 2x3 - 3x

Q: 3. Let h(x) be a twice-differentiable function with h'(x) < 0 and h" (x) < 0 for all real numbers x,…

A: Here, given that h'(x)&lt;0 for all x. Now,…

Q: Find the exact arc length of the curve over the stated interval. y = 3r/2 – 4, from a = 0 to a = 1…

A: The curve y=3x32-4, from x=0 to x=1

Q: Consider the following. -x2 – 4 f(x) = (a) State the domain of the function. all real numbers x…

A:

Q: QUESTION 1 At a price of $700 a supplier will supply 170 items. If the price decreases by $100, then…

A: Given query is to find linear function of supply.

Q: ニ1 近。 Question 2 D. O E OA 3. (A) 3. 3. (). 32 3. (C) 16. (B) zg (7) The area of the region enclosed…

A:

Q: 7. Consider the curve x 3t4 + 4t3 + 100, y = 3t - t°, -2 <t< 2. dy What is dx dy when t = 1? dx (a)…

A:

Q: plane

A: answer is in next step

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of h(z) = , • sin (z ) (cos…

A: A detailed solution is given below.

Q: Determine the interval(s) on which the graph of the function f(x) = a – 32? %3D is concave upward.…

A:

Q: 5. Determine the following limits. If infinite, specify ∞ or -o. If an answer does not exist,…

A:

Q: Given the following optimization problem: max(500-q)q-50q p*=275 O True O False

A:

Q: Q3/ Find the area of zone bounded by curves: y= x , y= 3x+8

A:

Q: The vat shown in the accompanying figure contains water to a depth of xo = 1.9 m. Find the work…

A: To find the work require to pump all the water to the top of the vat. Given, 9810N/m^3 as the weight…

Q: Find the work required to haul a load 100 feet by a 100lb force acting on the load at a 20° angle.…

A:

Q: Sx'e-2x* dx

A: ∫ x3e-2x4dxLet u=-2x4.=∫ -eu8du=-18·∫ euduSubstitute back u=-2x4=-18e-2x4Add a constant to the…

Q: A manufacture has been selling 1100 television sets a week at $420 each. A market survey indicates…

A:

Q: Directions: Solve the derivatives of the following functions using the rules in differentiation…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: (x³-4) dx x3+2x2+2x

A: Here we have to integrate the given Integral.

Q: Q3/ Find the area of zone bounded by curves: y= x² , y= 3x+8

A:

Q: NG) Find T(t) and N(t) at the given point. T r(t) = 8 cos(t)i + 8 sin(t)j+ tk; t = T()= NE) -| ||

A:

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A:

Q: 1-x² dx

A:

Q: Using a Taylor series, find the polynomial of least degree that will approximate F(x) throughout the…

A:

Q: 1. Find the Maclaurin series for the function x2 In(4+ x). Also find the associated radius of…

A:

Q: Find the area of the region bounded by y = ¾(x + 2), x = 2 and the x-axis.

A:

Q: Use quadratic formula to find all the real zeroes of the 2nd degree polynomials 6x²-x-1

A: The given polynomial,      6x2-x-1

Q: A wooden rectangular box is to be made having dimensions 3 ft, 4 ft, 5 ft. The cost of the wood to…

A: The error in the estimate of the cost of the wood is 120P

Q: 1- (2 xy-4 y) dx+(3x²y-8x) dy30

A:

Q: n the 3-o'clock direction.

A: answer is in next step

Q: 5- (tanx + secx)2 dx

A:

Q: Write the following first-order differential equations in simplified standard form. dy (5х + 3)у +…

A: We have to write the given first order differential equation in standard form .

Q: dy Solve dx x +y and find the particular solution when y(1) = 1 dy = x – y and find the particular…

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: The given expression for the volume of a tetrahedron is; V=16u·v×w And The vertices are P-6,7,0,…

Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

A:

Q: 12. y' = x2 - 2xy + y2

A: See the answer below

Q: Given the differential equation -7x y" + y' = 6x2 Use Reduction of Order and the letter "R" to…

A:

Q: d d Calculate ri(t)· r2(t)] and dt [ri(t) × r2(t)] first by differentiating dt the product directly…

A:

Q: Question 2 of 10 Find the exact arc length of the curvex= + 2) trom y= 0to y 5. Enter the exact…

A:

Q: r(1) = 2 Ans: In + = de II

A:

Q: 1+ cot(t) 1+ tan(t) Simplify to a single trig function with no fractions. Submit Question

A:

Q: iS dx Evaluate the integral improper integral (2x- 1)3 - 00 1/4

A: we have to find the integral.

Q: cos 2ot) Wheré w iš a -3(1-cosh 377t) 4.

A: Given problem :- 4.  -3(1-cosh377t)/t  Find laplace transformation of given f(t) function

Q: 3. x² + 5x + C .2

A: Derivative of xn is ddxxn=nxn-1.

Q: What is the derivative of the function f(x) = In(3x²) ? O a. f'(x)= 2 а. O b. None of these. 1…

A:

Q: ² V1-x² dx x2 Use trigonometric substitution

A:

Q: - answer to part (a), determine the inflection points of f. Each point should be entered as an…

A:

Q: 3. Compute the f(x, y) = 4x³ + 6xy² R=[1,3]x[-2,1]. iteration for the function on the rectangles

A:

Q: Find the absolute maximum and absolute minimum of 9(t) = t/4– t on the interval [0.8, 2.8]. Enter…

A: topic - application of derivatives

Q: 1. Find the maximum value of the function f(x.y)= 4x + 2y +x* - 2x*+ 2xy– 3y° on the interval –2 to…

A: Note: Only part b) comes under calculus. Part a) and part c) are not covered under calculus. Hence,…

Q: Use the power reduction formulas to rewrite the expression, sin2(6x)

A: Given query is to rewrite the expression.