Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative. u(2) = 7, u '(2) = 2, v(2) = -3, v '(2) = -4. at x = 2 dx u

Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

Q: 18. dx The integral - can be rewritten as V1 - x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī -s) s--00 s--00...

A:

Q: Find the second derivative of the function. 1+20 (2-0) 20

A:

Q: 7. Determine f(x) so that Scon cos(In°x)f(x) dx = sin(ln²x) + C 2 Inx (a) 2 In x (b) In x (c) (d) 2

A:

Q: Find the average rate of change for the following function. f(x) = 2x - 5x +3 between x = - 1 and x ...

A:

Q: Find the interval of convergence of the power series. (Be sure to ine your answer using set notation...

A:

Q: 7. This problem requires calculus. Let P = {a,x" + an–1x"-1 + ...+ a1x + ao | n > 0, ao, . ., an E R...

A: Given P is a set of polynomial function of degree n of real co-efficients and a function F:P→P such ...

Q: ts Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box...

A:

Q: 4. Ifu = f(x), then : dx = J x* + 2x² + 1 k + C for some constant k. x² + 1 Compute kf (1). (a) ¼ (b...

A:

Q: ue Theorem on the given interval? ction satisfies the Mean Value Theorem. continuous on [0, 3] and d...

A:

Q: 7Q b) TR = (Q+3)

A:

Q: Find the Taylor polynomials of orders n = 0.1,2, 3. and 4 about 2 = x, and then find the nth Taylor ...

A:

Q: Let P(x) = F(x)G(x) and Q(x) = F(x) where F and G are the functions whose grap G(x) y F 2 -1 4 8. Fi...

A:

Q: Calculate the respective marginal functions for the following total cost/revenue functions. you stat...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Learning Task 3: Find the equation of the tangent line to the following curves at a given point 1. y...

A: we need to find the tangent line of y=x2-6x+9 at x=2

Q: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: Instructions: Use Rules of Differentiation to differentiate the following functions. Show your solut...

A: Using product and division rule for differentiation. 

Q: Evaluate the integral: I = 2x S where the solid S is defined as: S = {(x, y, z) E R³ : x > 0; 0 < y ...

A:

Q: 15. Find the area between the curves x = y? - 4 and x = 8- 2y.

A:

Q: dx The integral can be rewritten as -∞ V1 – x (a) lim (-2+2vī1-s) (b) lim (-1+ 2v1 – s S--00 S--00 (...

A: Given ∫-∞0dx1-x Let t=1-x differentiating with respect to x, dt=-dx ∫-∞0dx1-x=-∫-∞0dtt=-∫-∞0(t)-1/2 ...

Q: Use sigma notation to write the Taylor series about x = xo for the functi e*; xo = 6 k=0 e6 k! k=0 k...

A:

Q: dx be given . If u = e* + 1, then the resulting integral is 2. Let | f(u) du. Compute f(3). (a) 2/3 ...

A:

Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for ...

A:

Q: x* – /x dx бу 4

A: integration

Q: z° – 6z' + 4z – 2 dz |

A:

Q: 0 Use an appropriate form of the chain rule to find dw/dt w = 5x²y°z*; x =², y = t², z = t°

A: As per our guidelines, we only solve one question.

Q: 11-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given inter...

A:

Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

A:

Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

A:

Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

A:

Q: Describe the sampling distribution of p. Assume the size of the population is 25,000. n= 600, p = 0....

A: Here given that, Population(N)=25000 n=600,p=0.1 Now, n≤0.05N600≤0.05*25000600≤1250 ............(1) ...

Q: 2 cot- (esc") if -3 3. a. Determine if f is continuous or discontinuous at x = 0 and at x = 3. If di...

A: For the solution of the problem follow the next steps.

Q: dx The integral | can be rewritten as V1. - X (a) lim (-2+2v1 – s) (b) lim (-1+2v1 – s) S--00 S--00 ...

A:

Q: 1+ In x 6. Find f(x) so that when u = f(x) the integral J tan(f(x)) dx can be rewritten as | cot u (...

A: Solve by integration

Q: To determine how fast a change in weight will occur, the most plausible assumption is that is propor...

A: Given that dwdt is proportional to the net excess C-19.25w

Q: the

A: We have to find the length of the given curve according to the given information

Q: SV + 2) /2 – 3y dy -

A: The detailed solution is given below Thank you 

Q: e2t+a (2 cos at – 3 cosh 2at) -

A:

Q: I have 1 yard piece of fabric with 45 inches width. I am planning to make hand towels out of it. If ...

A: Measurement

Q: Consider the function f(x) = 4x - 4x – 1 and complete parts (a) through (c). (a) Find f(a + h); f(a ...

A:

Q: 14. If we let u = 4x – 1 for the (2tan(4x-1)-3 cos“(4x=1) dx. what will be the cos(4x-1) resulting f...

A:

Q: when r = 5 and dt An expanding sphere has radius r = 0.6t cm at time t (in seconds). Let V be the sp...

A:

Q: rectangular carpet has an area of 220 yd^2 .The width of w is 9 yards less that the length l.find th...

A: Options are wrong I have given you correct answer

Q: Determine if the series converges or diverges. n=1 4+n3 The series (coverges/diverges) using the met...

A: The given series is ∑n=1∞n4+n3. We have to check whether the series is convergent or not. From the l...

Q: n+ In (3) Given the sequence Then the limit lim a = a

A:

Q: dx x Vx²+2x-1

A: Evaluate the integral∫1xx2+2x-1dx

Q: 2 tan(4x-1)–3 cos²(4x-1) dy cos(4x-1) 4. If we let u = 4x -1 for the ', what's going to be the resul...

A:

Q: u du Form Answer 5sinx dx Ex. J a+ 2cOsx 3+ 2cosx -2sinxdx uż du -5V3 + 2cosx + C 3 15. Given: •dx 5...

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) x2 n- 4, c-2 P4(x) -

A:

Q: C) Replace the following polar equation by equivalent Cartesian equation. rsine Inr + In cose %3D

A: We can replace the given polar equation by equivalent Cartesian equation as below.