1- 21 17. v' v(1) = - 2

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A: (a) To integrate: ∫ex2dx We know that, ex=1+x+x22!+x33!+⋯⋯=1+x+x22+x36+⋯⋯ Now, ex2=1+x2+x42+x66+…… T...

Q: Find the domain of the function : g(x) = 3/(x2 - 2x - 15)

A: Given: gx=3x2-2x-15 we know that for any given rational functionfx=pxqx domain is denominator is not...

Q: Let r(x) = f(g(x)) and s(x) = g( f(x)), where f and g are shown in the figure. Find (a) r′(1) and (b...

A: Given: r(x)=f(g(x)) and s(x)=g(f(x)) And the graph, To find: a) r'1 b) s'4

Q: Solve for A: C = A + Ar.

A: We have to solve for A for the equation: C=A+Ar Taking A common from A+Ar, we get C=A+ArC=A1+r Now d...

Q: Use familiar area formulas to evaluate the definite integral.

A: Given, ∫24(2x-3)dx

Q: Determine the area of the given region. The region in the first quadrant bounded by the curve Vx + V...

A: Given: x+y=1 region bounded by given curve can be drawn as below

Q: Evaluate the definite integral by the limit definition.

A: Given: ∫031-2x2dx

Q: The diagram shows the position of two lighthouses, A and B. A boat is in the sea. It is the same dis...

A:

Q: Add or subtract terms whenever possible. √20 + 6√5

A: Add or subtract terms whenever possible. √20 + 6√5

Q: Find the mass of the planet's atmosphere.

A:

Q: Solve the Attached problem ?

A: To Determine: solve the following initial value problem for u as a function of t  Given: we have a d...

Q: Evaluate the integrals ∫7 cos7 t dt

A: We have to evaluate the integral: ∫7 cos 7t dt Solving by substitution method, Assuming, z=7t Differ...

Q: 24. Find a parametrization of the lemniscate (x2 + y²)² = xy (see Figure 23) by using t = y/x as a p...

A: Given that,  x2+y22=xy      ...(1) And t=yx⇒y=xt

Q: Graphing functions a. Determine the domain and range of the following functions. b. Graph each funct...

A: Given: hx,y=x+yx-y

Q: Evaluate the integrals

A:

Q: Find the average value of the function on the giveninterval.   h(r)   = 3/ (1+ r) 2 , [1, 6]

A: hr=31+r2,  1, 6  

Q: Use the given vectors v = 3i + j, w = i + 3j to find v . w and v . v.

A: Given vectors - v = 3i+j         ................(1)w = i+3j      ..............(2)Part (a) - v.w = ...

Q: Computing directional derivatives with the gradient Compute the directional derivative of the follow...

A: Given, gx,y=sin π2x-y; P(-1,-1); 513,-1213

Q: DISCUSS: Algebraic Errors The left-hand column of the table lists some common algebraic errors. In e...

A: Need to find out counterexamples for the data

Q: A mathematics professor recently purchased a birthday cake for her son with the inscription Happy (2...

A: Given expression 252·234÷214 Simplify the product 252·234 252·234÷214=252+34÷214252·234÷214=2104+34÷...

Q: u = 2i + j − 2k, v = i − 3j + 2k , Find (a) u ∙ v, (b) u ∙ u, (c)|| v ||2 , (d) (u ∙ v)v, and (e) u ...

A: Given that, u=2i+j-2kv=i-3j+2k

Q: Find the indefinite integral and check the result by differentiation                     ∫x3(x4 + 3)...

A: ∫x3x4+32 dx Put, x4+3=t⇒4x3+0=dtdx⇒4x3 dx=dt⇒x3 dx=dt4 Therefore, ∫x3x4+32 dx=∫t2 dt4=14∫t2 dt=14·t3...

Q: Determine whether the given statement makes sense or does not make sense, and explain your reasoning...

A: Statement given is False.Reason -To find the rate of change of a function f(x) using graph, we need ...

Q: Determine whether the function is even, odd, or neither. Then find the zeros of the function. Use a ...

A: A function is said to be even if f(x)=f(-x) A function is said to be odd if f(x)=-f(-x) If above bot...

Q: A baseball is hit 3 feet above ground level at 100 feet per second and at an angle of 45° with respe...

A: Given data for the projectile motion of ball.Speed of ball = u = 100 feet/secProjectile angle = θ = ...

Q: Find the derivative of the function. y = sec7x/7 − sec5x/5

A: Consider the following equation: y=sec7x7-sec5x5 Differentiate y with respect to x: dydx=ddxsec7x7-s...

Q: Solve  y"-9y=0

A: Given the quadratic equation  y" - 9y = 0 We need to solve it  Now,  y" -9y = 0.     implies that  (...

Q: Solve the logarithmic equation log(x - 2) + log 5 = log 100. Be sure to reject any value of x that i...

A: Given logarithmic equation is, log(x - 2) + log 5 = log 100

Q: 30. Tree Diameter For a certain type of tree the diameter D (in feet) depends on the tree's age t (i...

A: Dt=5.41+2.9e-0.01t

Q: If f(x) = 7/(x - 4) and g(x) = 2/x, find (f ∘ g)(x) and the domain of f ∘ g.

A:

Q: How can we find the slope of the tangent line to the parabola y = x2 at the point?

A: Consider the following equation of parabola: y=x2 Differentiate y with respect to x: dydx=ddxx2=2x

Q: Find   (a) r′(t),    (b) r″(t),    (c) r′(t) ∙ r″(t), and     (d) r′(t) × r″(t). r(t) = t3i + (2t2 +...

A: Given rt=t3i+2t2+3j+3t-5k Power rule of differentiation states that: ddxxn=nxn-1 Differentiating the...

Q: The length of a violin string varies inversely as the frequency of its vibrations. A violin string 8...

A: Given that: The length of a violin string varies inversely as the frequency of its vibrations. A vio...

Q: Prove that the graph of the equation Ax2 + Cy2 + Dx + Ey + F = 0 is one of the following (except in ...

A: Given, The graph of the equation is, Ax2+Cy2+Dx+Ey+F=0 Let A=1, C=0 so that, x2+Dx+Ey+F=0 By complet...

Q: Example 1: Solve the system of linear equations using matrix inverse method. 5x +2y = 4 7x +3y = 5

A:

Q: Convert the rectangular equation x2 + y2 = 100 to a polar equation that expresses r in terms of θ.

A: Convert the rectangular equation x2 + y2 = 100 to a polar equation that expresses r in terms of θ.

Q: maximum and minimum

A: To find: The absolute extremum of the given function

Q: Find the limit. Use l’Hospital’s Rule where appropriate.If there is a more elementary method, consid...

A: Given: L=limx→11-x+lnx1+cosπx we know that if x→a, fa→0, ga→0 then by using L hospital's rule limx→a...

Q: Find the quadratic approximation to ƒ(x) = 1/(1 - x) atx = 0.

A: Given,  f(x) = 1/(1 - x) at x = 0

Q: Higher-order derivatives Find ƒ′(x), ƒ″(x), and ƒ‴(x).

A: Given, f(x)=x2(2+x-3)

Q: Solve and graph the solution set: (x + 1)/(x + 3) ≥ 2.

A: Given: (x+1)(x+3)≥2