(a) Any critical point of a function f is either a local maximum or local minimum for f. True False (b) Every differentiable function is continuous.

Q: 1 1-25t² dt

A:

Q: y=ex5

A:

Q: 7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes…

A:

Q: Prove that √1+i√3+√1-i√3 = √6

A:

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 8,…

A:

Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: 5sec 5 sec 5x tan 5x dx

A: Given, ∫5sec 5x sec 5x tan 5x dx

Q: 1. y=(sin ¹x² + X 1+tan x

A:

Q: Q2/ Find the velocity, speed, unit tangent vector and acceleration of the position vector f(t) at…

A: This is a problem related to vector and derivative of the function. Based on the general formula and…

Q: 5. (a) Use Newton's binomial theorem to calculate √50 with 4 terms.

A:

Q: Find the equation of the plane that passes through the points (3, -2, 2), (-9, 2, 4) and (-6, -4,…

A: We need to find equation of plane.

Q: Instructions 1. Write your complete solution for each item. It should be handwritten. 2. Make sure…

A:

Q: 1. f(x) da converges, then If f(x) ≤ g(x) for all z in [a, +∞o) and converges. g(x) dx also

A: Given

Q: _2. Which of the following series is divergent? 1 1 1 (α) Ση=12n-1 (b) En=1,3 (c) En=13 Σ n2 _3.…

A:

Q: (b) n 1+ (x-1)"; r=1/e Σ(1-1) η n=1

A: Here, the given series is: ∑n=1∞1+1nn2(x-1)n Let, an=1+1nn2(x-1)n; n≥1

Q: Find the arclength of r(t)= on the interval from t equals zero tot equals 2 times pi.

A: Given:  r(t)=<5cot(t), 3 sin(t), 4 sin(t)>To find:  Arc length form t=0 to t=2π

Q: 370 0 3sin²2x dx

A:

Q: Find the area under the curve 4x²-3x+6 between x = -2 and x=3

A:

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+ 32) sin(t)dt

A: We nee to evaluate ∫t3-4t2+5t+32 sin(t) dt

Q: For each of the following functions, do the following: a. Determine if f is continuous at a. b.…

A: We are authorized to solve only one question, please repost remaining questions Continuity and…

Q: Let u= -10i+4j- 4k, v= 5i-2j+2k, w=2j-5k. Which vectors, if any are (a) perpendicular? (b) Parallel?

A:

Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Differentiate the following function. f(x) = -3e-3x d -(-3e-³x) = dx

A:

Q: local linear (20) 1f the graph of the function f(x) is stretched vertically by a factor 2 and then…

A:

Q: Evaluatef (cot2x + 2tan²x - 5) dx a. cotx + 2tanx + 4x + C b. -tanx-2cotx - 4x + C c. -cotx 2tanx -…

A: I have stated the used formulas in the solution

Q: Solve the initial-value problem. x' + 7x = e-7t x(t) =| X cos(t), x(0) = -1

A:

Q: 10. f(x, y) = x/(x² + y²)

A:

Q: 2. Find the value of 1 3x + 13 x² + 4x +3 dx

A: We can you valve the given definite integral by using the partial fraction method.

Q: 1 (2m-3)√4m (m-3) dm

A: Given

Q: A poster of area 6000 cm² has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

A:

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

A:

Q: The table below shows values for four differentiable functions. Suppose we know the following…

A: Given

Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

A:

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

A:

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A:

Q: Which of the following statements is CORRECT? x³ + x 1 = 0 has no solution in [0, 2] Ox³ + x-1=0 has…

A:

Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

A:

Q: y" - y' - y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: Given :y''-y'-y=cos5t-sin5ty(0)=2 and y'(0)=5

Q: ¹-(₁ (1-2 (a) Given that A= (1) AB (ii) B (iii) AT 3 5 0 206 1 4 -1 3 ar and B= -3 2, determine

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the derivative of the following function. -9e 5x y= 4x + 3 y'(x) =

A:

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 5 about the x-axis.…

A:

Q: B. Find the area bounded by the given curves Show the graph (you can use any graphing software,…

A: A detailed solution is given below.

Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it…

A:

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

A:

Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32) sin(t)dt

A: The tabular integration is a process of evaluating the integral using integration by parts. In this…

Q: The order of differentiation in multiple integration of continuous integrand A. has six…

A: According to the Fubini's theorem "the  order of differentiation in mulple integration can be…

Q: Find the first derivative of f = (h+2)² (2h+1) h²+3 V using logarithmic differentiation

A: