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mathematics
precalculus 1st
Calculus For Scientists And Engineers Early Transcendentals 1st Edition William L Briggs, Bernard Gillett, Bill L Briggs, Lyle Cochran - Solutions
Find the first partial derivatives of the following functions. f(x, y, z) = xy + xz + yz
Find the indicated derivative for the following functions. az/ap, where z = x/y, x = p + q, and y = p - q
Find the first partial derivatives of the following functions. g(x, y, z) = 2x²y3xz4+10y2z 2
At what points of R2 are the following functions continuous? g(x, y) = ln (x - y)
At what points of R2 are the following functions continuous? f(x, y) = sin xy
Find the indicated derivative for the following functions. dw/dt, where w = xyz, x = 214, y = 3t¹, and z = 4t-3
Find the first partial derivatives of the following functions. Q(x, y, z) = tan xyz
Find the first partial derivatives of the following functions. h(x, y, z) = cos (x + y + z)
Find the indicated derivative for the following functions. aw/ax, where w = cos z cos x cos y + sin x sin y, and z = x + y
Find the indicated derivative for the following functions. az ax where 1 X + 1 y + 1 - Z 1
At what points of R2 are the following functions continuous? = cos (x + y) h(x, y) =
Find the first partial derivatives of the following functions. F(u, v, w) u v + w
At what points of R2 are the following functions continuous? p(x, y) || ex-y
Find the indicated derivative for the following functions. az/ax, where xy - z = 1.
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). f(x, y, z) = 2xyz - 3xz + 4yz
Find the first partial derivatives of the following functions. G(r, s, t) = √rs + rt + st
At what points of R2 are the following functions continuous? f(x, y) = ln (x² + y²) In
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). g(x, y, z) = 1 X-Z
Find the first partial derivatives of the following functions. g(w, x, y, z) = cos = cos (w + x) sin (y - z)
Find the first partial derivatives of the following functions. f(w, x, y, z) = w²xy² + xy³z²
At what points of R2 are the following functions continuous? 2 f(x, y) = √4x² - y²
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). p(x, y, z)=√x² + y² + z² - 9
Find the first partial derivatives of the following functions. h(w, x,y,z) = ZM ху
At what points of R2 are the following functions continuous? g(x, y) = √x² + y² - 9 2
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). Q(x, y, z) 10 2 2 1 + x² + y² + 4z²
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). f(x, y, z)= Vy - z
At what points of R2 are the following functions continuous? h(x, y) = √x - y 4
Find the first partial derivatives of the following functions. F(w, x, y, z) = w√x + 2y + 3z
Consider each of the following surfaces and the point P on the surface.a. Find the gradient of f.b. Let C' be the path of steepest descent on the surface beginning at P and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane. f(x, y) = 4 + x (a plane); P(4, 4, 8)
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). F(x, y, z)= Vy - x²
At what points of R2 are the following functions continuous? f(x, y) sin (x² + y²) 2 x² + y² if (x, y) = (0,0) if (x, y) = (0,0)
Consider each of the following surfaces and the point P on the surface.a. Find the gradient of f.b. Let C' be the path of steepest descent on the surface beginning at P and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane. f(x, y) = y + x (a plane); P(2, 2, 4)
At what points of R2 are the following functions continuous? f(x, y) = 1 - cos (x² + y²) x² + y² if (x, y) = (0,0) if (x, y) = (0,0)
Find the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin). 2 2 f(w, x, y, z) = V1 - w² 1-w²x² - y² - W N 2
Consider each of the following surfaces and the point P on the surface.a. Find the gradient of f.b. Let C' be the path of steepest descent on the surface beginning at P and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane. f(x, y) = 4x² - 2y²; P(1, 1, 1)
Evaluate the following limits. x¹/3 - yl/3 lim (x,y) (8,8) x2/3-y2/3
Evaluate the following limits. lim (x,y,z)→(1,In 2,3) zety
Consider each of the following surfaces and the point P on the surface.a. Find the gradient of f.b. Let C' be the path of steepest descent on the surface beginning at P and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane. f(x, y) = y + x ¹; P(1, 2, 3)
Evaluate the following limits. lim (x,y,z)→(0,1,0) In e¹² (1+y)
a. Determine the domain and range of the following functions.b. Graph each function using a graphing utility. Be sure to experiment with the window and orientation to give the best perspective of the surface. g(x, y) = exy
Consider the following functions f, points P, and unit vectors u.a. Compute the gradient of f and evaluate it at P.b. Find the unit vector in the direction of maximum increase of f at P.c. Find the rate of change of the function in the direction of maximum increase at P.d. Find the directional
Evaluate the following limits. yz - xy - xz - x² lim (x,y,z)→(1,1,1) yz + xy + xz - y²
a. Determine the domain and range of the following functions.b. Graph each function using a graphing utility. Be sure to experiment with the window and orientation to give the best perspective of the surface. f(x, y) = |xy|
Evaluate the following limits. x - √xz - √xy + Vyz lim (xy.z) (1,1,1) xVxz + √xy - Vyz
a. Determine the domain and range of the following functions.b. Graph each function using a graphing utility. Be sure to experiment with the window and orientation to give the best perspective of the surface. p(x, y) = 1 |x-1| + y + 1 −
Consider the following functions f, points P, and unit vectors u.a. Compute the gradient of f and evaluate it at P.b. Find the unit vector in the direction of maximum increase of f at P.c. Find the rate of change of the function in the direction of maximum increase at P.d. Find the directional
Functions Differentiate the following functions. r(t) = (cost, t², sin t)
Functions Differentiate the following functions. r(t) = (4e¹, 5, In t)
Functions Differentiate the following functions. r(t) = (2t³,6Vt, 3/t)
Functions Differentiate the following functions. r(t) = (tan t, sect, cos² t)
Functions Differentiate the following functions. r(t) = (te, t ln t, t cos t)
Functions Differentiate the following functions. r(t) = ((t + 1)¹, tan¹t, In (t + 1))
Functions Differentiate the following functions. r(t) = = (4,3 cos 2t, 2 sin 3t)
Functions Differentiate the following functions. r(t) = (e¹, 2e-4e²¹)
Compute the dot product of the vectors u and v, and find the angle between the vectors. u = (3, 4,0) and v = (0,4,5)
Compute the dot product of the vectors u and v, and find the angle between the vectors. = i and v = i + V3j u =
Compute the dot product of the vectors u and v, and find the angle between the vectors. u = √2i + √2 j and v = -√2i - √2j
LetCompute the derivative of the following functions. u(t) = 2t³i + (t² − 1)j – 8k and v(t) = e¹i + 2e¹¹j - e²¹k.
What is the magnitude of the cross product of two parallel vectors?
Compute the dot product of the vectors u and v, and find the angle between the vectors. u = 4i + 3j and v = 4i - 6j
Compute the dot product of the vectors u and v, and find the angle between the vectors. = (-10, 0, 4) and v = (1,2,3)
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) = 4 cos tj + 16 sin tk, for 0 ≤t≤ 2π
Compute the dot product of the vectors u and v, and find the angle between the vectors. u (3,-5, 2) and v = (-9,5, 1)
Compute the dot product of the vectors u and v, and find the angle between the vectors. u = 2i - 3k and v = i + 4j + 2k
LetCompute the derivative of the following functions. u(t) = 2t³i + (t² − 1)j – 8k and v(t) = e¹i + 2e¹¹j - e²¹k.
Compute the dot product of the vectors u and v, and find the angle between the vectors. u i 4j - 6k and v = 2i - 4j + 2k = −
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) 2 cos ti + 2 sin tj + 2k, for 0 ≤ t ≤ 2π
LetCompute the derivative of the following functions. u(t) = 2t³i + (t² − 1)j – 8k and v(t) = e¹i + 2e¹¹j - e²¹k.
LetCompute the derivative of the following functions. u(t) = 2t³i + (t² − 1)j – 8k and v(t) = e¹i + 2e¹¹j - e²¹k.
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) t cos ti t sin tj + tk, for 0 ≤ t ≤ 6T
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) = cos ti+j+ sin tk, for 0 ≤ t ≤ 2π
For the given vectors u and v, calculate projvu and scalvu. = (5, 0, 15) and v = (0,4,-2)
LetCompute the derivative of the following functions. u(t) = 2t³i + (t² − 1)j – 8k and v(t) = e¹i + 2e¹¹j - e²¹k.
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) = e ¹/20 sin ti + et/20 cos tj + tk, for 0 ≤ t < ∞
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) = 4 sin ti + 4 cos tj + e/10k, for 0 ≤ t < ∞
Graph the curves described by the following functions, indicating the direction of positive orientation. Try to anticipate the shape of the curve before using a graphing utility. r(t) = et/10i + 3 cos tj + 3 sin tk, for 0 ≤ t < ∞
For the given vectors u and v, calculate projvu and scalvu. u = 5i + j - 5 k and v = i + j - 2 k
LetCompute the derivative of the following functions. u(t) = 2t³i + (t² − 1)j – 8k and v(t) = e¹i + 2e¹¹j - e²¹k.
For the given vectors u and v, calculate projvu and scalvu. u = i + 4j + 7k and v= 2i - 4j + 2k
Compute the following derivatives. [(3t² i + √tj − 2t¯¹k). (cos ti+ sin 2tj - 3tk)] dt
Compute the following derivatives. d [(t³i + 6j − 2√tk) × (3ti - 12t²j - 6t-²k)] dt
Evaluate the following limits. lim cos 2ti 4 sin tj + 1π/2 2t -k TT
Compute the following derivatives. d [t²(i + 2j − 2tk) · (e¹i + 2e¹j − 3e¯¹k)] dt
Compute the following derivatives. d -[(t³i – 2tj – 2k) × (ti – t²j – t³k)] - - dt
Compute r"(t) and r"'(t) for the following functions. r(t) = Vt + 4i + t ¡¡ — e¯¹¹k t + 1
Evaluate the following limits. lim (2e¹i +6e¹j - 4e-²¹k) t→In 2
Evaluate the following limits. lim ei 2t t + 1 j + tan ¹tk
Evaluate the following limits. t lim 1-21²2² +1 -i-4e¹ sint j + 1 √4t + 1 k
Compute the indefinite integral of the following functions. r(t) = (1³3t, 2t - 1, 10)
Evaluate the following limits. lim 1-0 sin t t i - et - 1 t -j + cost + 1²/2 - 1 2 -k
Evaluate the following limits. tan t lim 1-0 t i - 3t sin t + vt + 1 k
Compute the indefinite integral of the following functions. r(t) = 2¹i + 1 1 + 2t j + In tk
Compute the indefinite integral of the following functions. r(t) = te¹i + t sin t²j 21 √₁² + 4 k
Find the function r that satisfies the given condition. r'(t) = (0, 2, 2t); r(1) = (4,3,-5)
Compute the indefinite integral of the following functions. r(t) = e³ti + 1 1 + 1² j 1 =k /2t
Find the function r that satisfies the given condition. r' (t) = (e¹, sin t, sec² t); r(0) = (2,2,2)
Find the domains of the following vector-valued functions. r(t) 2 t - 1 i+ 3 t + 2 -j
Find the function r that satisfies the given condition. r' (t) = (e²¹, 12e-¹, 1- 2e¹); r(0) = (1, 1, 1)
Find the function r that satisfies the given condition. r' (t) = (1, 2t, 3t²); r(1) =(4,3,-5)
Find the function r that satisfies the given condition. r' (t) = (Vt, cos nt, 4/t); r(1) = (2, 3, 4)
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